Is Mrs. Jones rich in "Thank You M'am?"
Mrs. Jones is not rich. This is demonstrated in the simple way she lives.
Although Mrs. Jones does give Roger the money for the shoes, it is not because she is rich. She gives him the money because she feels an affinity for him, and she empathizes with his situation.
Mrs. Jones lives in a small apartment furnished with a kitchenette. This demonstrates that she is not wealthy enough to have a house or even full-sized apartment.
When she got to her door, she dragged the boy inside, down a hall, and into a large kitchenette-furnished room at the rear of the house. She switched on the light and left the door open.
We also know that she is not the only in the “large house” and shares it with “other roomers.” We can assume it is a one-room apartment because the main room has has a bed in it, although the room is described as “large” so she’s not terribly poor.
Mrs. Jones lives a comfortable, simple life. This is also demonstrated in what she feeds him—canned milk, lima beans, and ham. Mrs. Jones explains that she works long hours at a hotel beauty shop.