A static character is one who does not undergo any significant change over the course of the story, novel or play in which the character appears. In "Thank You Ma'am," Mrs. Luella Bates Washington Jones is a consistently strong-minded and strong-willed character from the beginning of the story to the end.

When the boy, Roger, tries to snatch her purse, Mrs. Jones kicks him in the behind and drags him to her home, questioning him as they walk. She is not the least bit rattled and takes complete command of the situation. Her physical strength matches her will, and it is no problem for her to keep Roger subdued.

Mrs. Jones also possesses a strong sense of morality. She knows that it was wrong of Roger to try to steal from her, but she also recognizes that he is a child who is being neglected at home and suffering with poverty. Her strong sense of morality guides her to help Roger by feeding him and helping him clean himself up before she gives him a bit of money and sends him on his way. Mrs. Jones's strong and matter-of-fact disposition is consistent from the exposition to conclusion of the story.

The answer to your question is simply a matter of applying the definition of the term "static character" to the character of the older woman in Langston Hughes' short story.

The enotes guide to writing character analyses (see the link below for the full guide) defines "static character" in these terms: "A character is considered flat (or static) when he or she does not experience change of any kind, does not grow from beginning to end."

The young man in the story clearly experiences a change in his awareness. The old woman does not experience a change. She's kind, generous, compassionate, etc. from the beginning to the story's end.