I would not call Mrs. Jones as rich or excessively wealthy. I think that this is not Hughes' primary motivation as the writer. Her presence is more effective if she is of moderate means, reflective of Roger's predicament. There are a couple of elements that makes us understand this. The first is that she is out late at night, with little to indicate that she is going "out on the town." Her residence seems to be an apartment as opposed to a palatial mansion. At the same time, the food that she cooks for her and Roger is not excessively ornate or elaborate. She warms up beans on an open stove that is more like a hot plate than anything else. Consider the analysis from enotes, itself:
Merely alluding to the economic problems that cause widows to work late shifts and parents to leave unemployed teenagers unsupervised, Langston Hughes focuses on the universal power of love and trust in “Thank You, M’am.”
In another sense, I wouldn't consider Mrs. Jones rich because of her generosity to Roger. It seems as if she has a certain empathy with Roger because of their shared financial condition. She disapproves of Roger's attempt to take the pocketbook, but she also understands the temptation that motivated why he did what he did. When she reflects about her own life, the recollections indicate a lack of wealth, which makes her giving Roger the money even more poignant precisely because she is not wealthy. She wishes to help Roger more than anything else, from one person who is economically challenged to another, indicating that social solidarity can be evident despite stressful financial conditions.