Mrs. Jones displays her motherly character in the way she addresses Roger and the way she holds him accountable for his actions.
When she catches him in the act of stealing her purse, she interrogates him about his motives. While she talks to him, Mrs. Jones keeps her hold on Roger; essentially, she doesn't let go of him until they reach her house. There, she expects him to wash his face before he comes to the table for a meal. Like a mother often does, Mrs. Jones lectures Roger about doing the right thing, even when he wants something he can't have.
In combination with her stern attitudes about theft, Mrs. Jones also exerts a compassionate maternal influence on Roger during the short time he is with her. For dessert, she shares a small cake with him; she feeds him well and even gives him ten dollars to purchase the blue suede shoes he has his eye on. Mrs. Jones never patronizes Roger or tries to shame him; she admits to him that, when she was young, she also wanted things she couldn't afford.
She is a powerful presence in Roger's life for a brief time; the combination of her compassion, sternness, and generosity so affect Roger that he is barely able to thank her before he leaves. The text tells us that Roger never sees Mrs. Jones again, but it is very likely that her powerful example will serve as a positive influence on Roger for the rest of his life.
Luella Bates Washington Jones, in Thank You M'am, is a character who reveals contradictory traits. The reader is immediately introduced to an imposing woman, which fact is clear from the contents of her purse where she keeps everything except "hammer and nails." She takes no nonsense and wants to teach the boy a lesson but, at the same time, has compassion and empathy with him.
This leads to an understanding that she is powerful which is reinforced by the boy's efforts to release himself - unsuccessfully - from her grasp. She also has an inner power which can be seen when "Roger looked at the door—looked at the woman—looked at the door—and went to the sink."
Roger wonders whether Luella is going to take him to jail but she has noticed his dirty face and her concern for him is genuine and motherly and "I got a great mind to wash your face for you" makes this clear. She goes on to mention how she would teach him right from wrong if he were her son.
All these characteristics build an image of a strong woman who is not judgemental but helpful and kind-hearted despite her exterior appearance.