It may not be easy to say that Tom's Wife is literally a symbol for greed - when characters are used as symbols, those characters are often supernatural or less directly involved in the more pedestrian details of the story, in essence reducing their characterization so that their role as a literary device is more apparent and easier to understand. For example, when Hamlet's father appears as a ghost, his lack of speech helps to establish him as a symbol rather than a fully-fledged character. However, in general it's more common for inanimate objects to be symbols.
Tom's wife can at least be said to represent greed or to be strongly driven by it. This is evidenced both by the narrator's initial description of her as miserly, and unable to share even the simplest of things with her husband, and by her later insistence on making the deal with Scratch to acquire the treasure. She appears to be motivated by nothing other than greed, with perhaps the exception of antagonizing her husband. In this way, we might say that she is a less than realistic character because of her limited behavior and personality, and this helps to interpret her behavior as symbolic; she is more of a personification of greed.