This is my first attempt at writing an answer, so I hope I have done it right in terms of links of attribution and format. If I have not, I hope someone will tell me, so I can benefit from clarification. Beyond that, I’ll simply give it a whirl!
Perhaps this is too simplistic and pedestrian of an interpretation, but maybe we can make a case for simplicity. It seems that the entire first verse is the antecedent referent for the phrase “a heap of broken images.” The phrase in question might best be studied by the words that immediately precede it: “Son of man, You cannot say, or guess, for you know only A heap of broken images…”
So, the first verse is fascinating because it contemplates the utter cruelty of a month that births beauty, and all the subsequent moments of beauty in a life, all the half stories, “mixing memory and desire,” mixing what we recall with what we wish, perhaps. But as this verse is entitled, The Burial of the Dead, we see a foreshadowing of some point, some perspective, some lesson that is almost tangible, albeit it with ‘broken images’—the earthy erosion, snow, rain, tubers, lilacs, a girl named Marie.
(As an aside that may or may not be relevant, but which requires discussion in another direction, it might help to know that a dear friend of Eliot’s died in the month of April during WWI. Eliot mourned deeply for his friend. Like I said, that takes it in another direction, a direction potentially important enough to rquire its own discussion for some other time.)(But if curiosity is killing you, this New Yorker article is excellent and cites original sources)
In an overall sense, that foreshadowed point, that message or lesson, is: Despite all the life we have and think we remember, whether we live it well or not, whether we remember it accurately or not, it is all for naught if we do not accept that we have one job on earth. That job, apparently, is to face the inevitable end of that life with a gratitude and gracious acceptance of the Higher Power that has made it all possible.
I get this notion from the words, “Son of man,” which was a reference to a verse in Ezekiel: “And he said unto me, Son of man, stand upon thy feet, and I will speak unto thee.” There are recurring “Son of man” references in Ezekiel.
The basic message of that Biblical reference is ‘Yes, it is all doom and gloom and the people will fight and write books about it, and bend the knee to false images and some will fight harder than others for their right to glorify said images. In the end, though, we ought to rejoice in the behavior that celebrates God’s word—having done so is the reward, the goal, the point of it all.’
Then Eliot gives us this:
“And the dead tree gives no shelter, the cricket no relief,
And the dry stone no sound of water.”
This appears to be a half-formed holographic Biblical reference to Ecclesiastics [12.5]: “Also when they shall be afraid of that which is high, and fears shall be in the way, and the almond tree shall flourish, and the grasshopper shall be a burden, and desire shall fail: because man goeth to his long home, and the mourners go about the streets…”
Ecclesiastics: 13,14 sums it all up this way: “Let us hear the conclusion of the whole matter: Fear God, and keep his commandments: for this is the whole duty of man. For God shall bring every work into judgment, with every secret thing, whether it be good, or whether it be evil.”
It’s worth noting that Eliot underwent a “conversion” of sorts to Anglo-Catholicism, an Anglican form of Christianity that emphasizes the Catholic rather than Protestant heritage and even customs. But he was very selective and discerning in his faith, and it didn’t happen overnight. Still, he was resolute and dedicated. His pursuit of faith was neither an overnight miracle nor was it something he dropped for the next new thing. It was a life-long pursuit for Eliot.
So, what the heck does all this have to do with “A heap of broken images?”
Plenty as it turns out. There is mention of Marie. Briefly, she was Marie, Countess Larisch. Cousin to Crown Prince Rudolph (who was also an Archduke), famous for the apparent murder suicide of his mistress, Baroness Mary Vetsera, and himself. There remains considerable controversy over whether it was, in fact, a murder-suicide, or a couple of murders. It seems that from the moment of the deaths, a cover up was well underway. Either way, it was forevermore ‘The Mayerling Affair’, as the doomed couple was staying at Mayerling Lodge when they left earth. Marie, the Countess Larich, was a close friend of Baroness Vetsera, and after the deaths, it was discovered she acted as a kind of go between for cousin Rudolph and Mary.
Marie was banished from court and spent the rest of her life in varying degrees of scandal, poverty and something less than palaces.
(You may be familiar with popular film culture that presents the basics, fictionalized and otherwise, of the Mayerling saga, namely Mayerling (1969) - This remake of the 1937 French favorite stars Omar Sharif as the Prince of Hapsburg, who defies his father by leaving his royal lifestyle and joining in student protests during the Hungarian Revolution. When he falls in love with the young and wealthy Catherine Deneuve, the king thwarts their plans of marriage, which leads to tragedy. Also starring James Mason and Ava Gardner. Also, in theater, Joseph and David Zellnik wrote City of Dreams, an original musical based on what the musical calls “the double suicide” of Crown Prince Rudolf and his teenage mistress, Mary, in Vienna in 1889 and which includes the character of Countess Larich.)
And guess what? T.S. Eliot met Countess Marie Larich, probably in 1911 near Munich—he was about 22 and she was 53. They spoke. The bulk of the first verse of The Wasteland were her memories, her conversation, her heap of broken images—and what a heap it was! Most of the lines of the first verse of The Wasteland were remembered snippets of conversations he had with Marie, according to Eliot’s second wife, Valarie Eliot. (Can be seen here, too). (Further, see the voluminous sites created by Richard A. Parker for information on Countess Marie Larisch, who wrote several books, including one about her involvement in the Mayerling Affair, an involvement she largely denied but which cost her the position as intimate and confident to her aunt Empress Elisabeth, Crown Prince Rudolph’s mother.
So! T. S. Eliot, who later became a Christian, surely began his search for “the answer” years before he tried to be a Christian. (And he prevailed in this attempt despite his rather unchristian like treatment of his first wife and collaborator, Vivien Haigh-Wood, a bright and creative, if tormented, troubled and emotionally damaged, woman. Eliot seemed not so much in love as he was desirous of losing his virginity.) Speaking of which, his friends (largely, the Bloomsbury clique) did not like Vivienne; Virginia Wolf once referred to her, as "This bag of ferrets is what Tom wears round his neck." (She, of course, later strolled along the banks of the River Ouse before wading in over her head with stones in her pockets.)
His search for faith, his unhappy marriage, his utter disillusionment with the war all combined to form what Ezra Pound, a friend and critic, saw as Eliot poetry that could be trimmed, edited, reworked and enhanced to become a major part of the Modernist literary movement that defined some of the greatest writing in our history. Eliot’s poetry began as far more autobiographical than it became in its final forms. By the time we read the leaner versions, including The Wasteland, we had real T.S. Eliot poetry, real sets of poems, yes, but one could say that we, too, had only “a heap of broken images” belonging to someone else and someone else’s someone else. Which reminds me of another verse from Ecclesiastics (12.8): “Vanity of vanities, saith the preacher; all is vanity.”