Tom and his wife fight constantly; this is a significant component not only of their relationship but their relevance and role in the story. Part of the reason for their fighting is that Tom's wife is greedy; the story states (perhaps metaphorically, but this is unclear) that a hen could not so much as lay an egg without Tom's wife taking the egg and hiding it somewhere to keep it away from Tom. It's never clear why she's this greedy, but the story has an overall moralistic tone, and it's common in such stories for characters to exhibit vices "just because" in order to keep the focus upon the detriments of those vices.
Greed affects Tom's wife because he confides in her about his meeting and bargain with Old Scratch, and how it might make them rich. His wife is overcome with desire for the treasure, basically ignoring the fact that the Devil is involved in the bargain, and sees only the potential for further hoarding. When Tom obstinately refuses to make the deal, his wife attempts to go in his stead, make the deal on her own, and secure the treasure for herself.
However, it's clear from the outcome that Scratch had no intention of cutting a deal with her, and she is removed from the story, perhaps as a sign of the corrupting influence of greed, and how her vices were too simplistic to afford her a further role in Scratch's plans.