TL;DR: Aphrodite has disguised herself as a worker in wool, an occupation which Rouse stereotypes as northern English.
Aphrodite’s speech here is book III, lines 390–394:
δεῦρ᾽ ἴθ᾽: Ἀλέξανδρός σε καλεῖ οἶκον δὲ νέεσθαι.
κεῖνος ὅ γ᾽ ἐν θαλάμῳ καὶ δινωτοῖσι λέχεσσι
κάλλεΐ τε στίλβων καὶ εἵμασιν: οὐδέ κε φαίης
ἀνδρὶ μαχεσσάμενον τόν γ᾽ ἐλθεῖν, ἀλλὰ χορὸν δὲ
ἔρχεσθ᾽, ἠὲ χοροῖο νέον λήγοντα καθίζειν.
Here’s a selection of translations:
“Come here; Alexander calls you to go home. There he is in his chamber and on his inlaid bed, gleaming with beauty and garments. You would not say that he had come there from fighting with a foe, but rather that he was going to the dance, or was sitting there having just recently ceased from the dance.”
A. T. Murray (1924), p. 157.
“Come hither; Alexandrus says you are to go to the house; he is on his bed in his own room, radiant with beauty and dressed in gorgeous apparel. No one would think he had just come from fighting, but rather that he was going to a dance, or had done dancing and was sitting down.”
Samuel Butler (1925), p. 48.
“Quickly—Paris is calling for you, come back home!
There he is in the bedroom, the bed with inlaid rings—
he’s glistening in all his beauty and his robes!
You’d never dream he’s come from fighting a man,
you’d think he’s off to a dance or slipped away
from the dancing, stretching out at ease.”
Robert Fagles (1990), p. 141.
So why did Rouse use dialect spelling for this speech? Here are some possibilities:
Aphrodite’s speech is dialectal in the original Greek? I doubt this. None of the other translators I consulted used dialect. The line notes by Thomas D. Seymour and Allen Rogers Benner (see the Perseus Digital Library) do not mention anything of the sort.
Aphrodite disguised herself as a woman of Lacedaimon (Sparta), and Rouse represents Spartan dialect as an English dialect? The trouble with this idea is that Helen also grew up in Sparta (she is the daughter of Leda, queen of Sparta), and her speech is unmarked in Rouse’s translation.
Aphrodite has disguised herself as a worker in wool (εἰροκόμος), and woollen manufacture is stereotypically carried out in the north of England, so that Rouse gives her a northern English dialect? The OED says that the spelling “tha” for “thou” is “English regional (chiefly northern)” and “thi” for “the” is “(Northumberland)”.
So, of these possibilities, (3) seems the most likely.
(A note on “that’st”. I think Rouse intends this to represent “thou wouldst”, but if so, “tha’dst” would be the more usual dialect spelling. Compare Haworth’s (1907) by Frances Hodgson Burnett: “Tha’dst mak’ a better rich mon than Haworth’s.”)