After some reflection, the simple answer may be that
- the Dog is the friend that is also foe
This assessment is based on the capitalization of Dog, and mythological conception of Sirius, the "dog star" that appears in time of harvest (a boon to mankind) but is also believed to bring madness, disease and death [Iliad 22.1].
This reference from Homer is consistent with the harvest theme of the passage, and the seemingly inconsistency of keeping "far hence" the "friend to men".
The scope of the poem is broad, and there is room for a range of more specific interpretations, but the horror of the first World War cannot be discarded--the Waste Land was published just 4 years after the conclusion of the man-made catastrophe and the global flu pandemic that followed.
The dog could symbolize war or the aftermath of war, or the instinctual nature of humans (bestial aspect in a benign form) blithely digging at the skeletons of the recent past (i.e. resurrecting "the horror".)
The Baudelaire quote at the end carries the implication that the Other, the "foe", is also the self, thus the Dog, Stetson and the narrator are all reflections of each other--man is man's greatest foe.
- the Dog represents the bestial nature of man
This supports the friend/foe idea, and is further supported by a main theme of Eliot's poetry in general, and this poem and the Four Quartets in particular, about the conflict between the material and the ideal world, i.e. the conflict between the flesh and the spirit.
The preceding passages are directly related to the excerpt and critical in interpreting it. They provide the setting:
Under the brown fog of a winter dawn,
A crowd flowed over London Bridge, so many,
I had not thought death had undone so many.
Sighs, short and infrequent, were exhaled,
And each man fixed his eyes before his feet.
Flowed up the hill and down King William Street,
To where Saint Mary Woolnoth kept the hours
With a dead sound on the final stroke of nine.
There I saw one I knew, and stopped him, crying “Stetson!
You who were with me in the ships at Mylae!
That corpse you planted last year in your garden,
Has it begun to sprout? Will it bloom this year?
The Waste Land, Section I: The Burial of The Dead
The Wasteland is about spiritual emptiness in an industrialized society still reeling from the carnage of World War I.
Eliot presents purgatorial imagery--an unreal city devoid of sunlight occupied by the living dead, spiritually exhausted (eyes fixed upon their feet as opposed to the heavens[A]), streaming across a bridge on their way to work.
King William Street is key--this is the historical center of the London banking district. The deadening bells of St Mary Woolnoth deepen choice--Eliot is presenting a church enforcing the strictures of an industry that is the opposite of religion[B], focused entirely on worldly gain, absent remorse.
Blake's London is partly about self-enslavement, partly about dehumanization in an industrial society, and Garden of Love is about the inversion of love in the context of religion. Baudelaire's Au Lecteur, upon which this section ends, is the most obvious referent:
Among the jackals, vultures, scorpions, snales and vermin,
There is one more ugly, more wicked, more filthy!
Which never makes great gestures or loud cries
Who would gladly reduce the earth to ruin
And yawning, swallow up the world:
Ennui, eyes loaded with involuntary tears,
Who smokes a hookah and dreams of the scaffold
"To the Reader", Charles Baudelaire
Ennui, in this poem also a proper noun ("C'est l'Ennui!"), is often translated as mere boredom, but that is the most benign definition. It may make more sense in Baudelaire, who is jaded, but in reference to The Wasteland, stronger definitions apply:
Ennervation, a feeling of being drained of vitality; fatigue.
Lassitude, a state of physical or mental weariness.
Apathy, a lack of concern.
Indifference, lack of sympathy.
Acedia, mental or spiritual apathy.
Baudelaire's Ennui is more sinister for "dreaming of the scaffold", which can have several meanings, all related to a love of death, including the guillotine (violent, bloody upheaval), and even one's own destruction (death wish).
This essay, speculating on the seemingly anomalous choice of "Stetson", notes that Valerie Eliot explained the character as "not referring to anyone in particular, but simply [meaning] any superior bank clerk: a person in a bowler hat, black jacket and striped trousers."[C]
I can't say if TS thought WWI was a conflict caused by bankers, but it was certainly a devastating war fought for no good reason, and the best explanation I've come across is John Keegan's assertion in A History of Warfare that the cause was simply that Europe was a powder keg after a century of massive armament in the wake of the success of the regimental system. Banking, in part, arose as a means of allowing sovereigns to fund wars with debt.
War is certainly related to this passage in the reference to Mylae--the Battle of Mylae was Rome's first great naval triumph (Britain's power was based on it's navy), directly led to subsequent conflicts (there were 3 Punic Wars), and was one of the largest conflicts in history at the time between the two dominant military/economic powers.
The relationship of money and conflict/dehumanization would seem to be theme of these passages and of the Wasteland overall.
Carthage, which was razed after defeat in the Punic Wars, is subsequently referenced in Section III of The Waste Land, The Fire Sermon, but the allusion carries a double meaning in that Dido, legendary Queen of Carthage, famously immolates herself for love after Aeneas leaves her to found Rome. (Purgation, and in particular, the convolution of love and fire, are the central theme of Eliot's later Four Quartets, largely composed during the time of the bombing raids on London in the second World War.)
The emptiness of material gain in the face of mortality is unequivocally demonstrated later in the poem:
Phlebas the Phoenician, a fortnight dead,
Forgot the cry of gulls, and the deep seas swell
And the profit and loss.
The Waste Land, Section IV: Death By Water
But the death is not entirely literal:
A current under sea
Picked his bones in whispers. As he rose and fell
He passed the stages of his age and youth
Entering the whirlpool.
Phlebas is both living and dead, a metaphor for the dehumanized condition of people in the modern era. Eliot goes Ozymandias for the conclusion of the passage, to reinforce his point as to the folly:
Gentile or Jew
O you who turn the wheel and look to windward,
Consider Phlebas, who was once handsome and tall as you.
"Gentile and Jew" is also not meant to be taken entirely literally, but as an inclusion of the Other (the Jew) in the family of man. The adversary is yourself, which is also the final implication of the Baudelaire:
You know him, reader, this delicate monster
Hypocrite reader, my semblance, my friend.[D]
"To the Reader", Charles Baudelaire
ON THE DOG
Imagery of dogs is related to ruin in the Iliad, which begins:
Of the mania sing, Goddess, of Peleus’ godlike son Achilles, [E]
the terrible destruction, the agony laid on countless Achaeans,
the multitude of stalwart souls cast into Hell before their time,
of the bodies of heroes spoil, for vultures and hounds
That’s pretty f---ing hardcore, and no accident Homer leads to Euripides, the Iliad to the Trojan Women. Notice in particular there is no mention of Trojans in these opening lines of the Iliad, but only of the Greeks themselves, and their suffering and shame.[F]
- the Dog represents the friend that is also foe
Which may also be the self, or humanity in general. The dog is also a reflection of the bestial part of ourselves, taking a benign appearance.
- the Dog digging up the remains may indicate the danger of revisiting past destruction
The body in the grave could be the first World War, and the potential threat of a reprise.
- the question of "Has it begun to sprout? Will it bloom this year?" reinforces the idea gain derived from the death
Normally, this would be cycle of life type stuff, generation out of destruction, a major theme in the later Four Quartets, but not in The Waste Land, in the wake of the deadliest calamity in human history up to that point.
This is not merely a comment on the First World War, or even of wars exclusively, but on the history of mankind in general, and the relationship, in many cases, of inhumanity to material gain.
Even in the face of, or wake of, destruction, the banker's primary concern is the bottom line. The blitheness of the passage reinforces the concept of casual inhumanity, which may be the greatest horror of all.
ON THE CAPITALIZATION OF DOG
Capitalization suggests a proper noun. Offhand, I can think of two relevant allusions, both deriving from Greek mythology:
Legendary hound who leads Erigone to the grave of Icarius. On discovering it, both the hound and Erigone leap from a cliff to their death. Hecuba, Queen of Troy, in one account is said to transform into the Maera[G] over grief for her lost children. In that form, the Maera is understood as a curse--the "black bitch of the sea" who brings death --relating to the aquatic theme in The Waste Land.
"...even so fast and furiously did the limbs of Achilles bear him onwards. King Priam was first to note him as he scoured the plain, all radiant as the star which men call Orion's Hound, and whose beams blaze forth in time of harvest more brilliantly than those of any other that shines by night; brightest of them all though he be, he yet sends an ill sign for mortals, for he brings fire and fever in his train - even so did Achilles' armor gleam on his breast as he sped onwards."
Iliad, Book 22
Here, Achilles the Destroyer is the dog of war, a symbol of progress rushing relentlessly onward, but ultimately doomed.
[A] Looking upward to God was very famously reinforced by Donne in the Holy Sonnets "Thou Hast Made Me, And Shall Thy Work Decay": "I dare not move my dim eyes any way, / Despair behind, and death before doth cast / Such terror, and my feebled flesh doth waste / By sin in it, which it towards hell doth weigh. / Only thou art above, and when towards thee / By thy leave I can look, I rise again;" Eliot wrote a book on The Varieties of Metaphysical Poetry which discusses Dante and Donne. I don't know if the title is intentionally a reference to William James' earlier and highly influential The Varieties of Religious Experience, but it seems not unlikely.
[B] "And Jesus went into the temple of God, and cast out all them that sold and bought in the temple, and overthrew the tables of the moneychangers, and the seats of them that sold doves, And said unto them, It is written, My house shall be called the house of prayer; but ye have made it a den of thieves." Matthew 21:12–13
[C] The linked image depicts a vintage Mallory Stetson derby bowler hat. I personally like to think that Eliot, who was originally American, and would have certainly been aware of the gunslingers mythos of the Old West, was using that term to give a sort of frontier feel. Modern financialism, and financialism in general, has always been, in part, about "pushing the envelope". (Successfully pushing the envelop includes management of risk.)
[D] Baudelaire uses “mon semblable”, translated as “my fellow” by Google. “Semblable” in English means “counterpart” or “equal”. In contemporary English, semblance is typically used in a pejorative sense, as in “similar in appearance but not in reality”, but the traditional usage is simple “resemblance”.
[E] Achilles "mania" is generally translated, not improperly, as “rage” and “wrath”, but I think in this context, the direct rendering of the greek μῆνιν (mania) is more instructive. Here mania can mean obsession, excessive exuberance, overactivity detrimental to one's health, (Achilles' mania has fatal consequences;)
[F] The dread of having one's body unburied and defiled is related to its shamefulness in an honor culture.
[G] From Euripides' Hecuba:
It will soon cease, when ocean's flood—
Shall convey me to the shores of Hellas?
No, but will close over you when you fall from the masthead.
Who will force me to take the leap?
Of your own accord you will climb the ship's mast.
With wings upon my back, or by what means?
You will become a dog with fiery glare.
Dead or alive shall I complete my life here?
Dead; and to your tomb shall be given a name—
Recalling my form, or what will you tell me?
“The hapless hound's grave,” a mark for mariners.