In the short story "Thank You, Ma'm," why did Mrs. Jones have Roger wash his face?

Although Langston Hughes does not explicitly tell us why Mrs. Jones makes Roger wash his face in “Thank you, Ma’m,” we can certainly infer the reason from the story.  We can infer that Mrs. Jones makes Roger wash his face in order to help instill in him a sense of pride and self-worth.
In this story, Mrs. Jones is clearly trying to reform Roger by making him respect himself.  After she initially kicks and shakes him, she stops trying to punish him much and instead tries to rehabilitate him.  When she takes him home, she repeatedly leaves him alone in such a way that he could both take her money and escape.  She is clearly trying to make him feel better about himself so that he will stop trying to commit crimes.
Once we understand this, we can see why Mrs. Jones has Roger wash his face.  His dirty face is a symbol of his life in general.  It shows that he does not respect himself enough to keep clean and it shows that his upbringing has been poor because he has no one at home to teach him to keep clean.  Mrs. Jones wants to reverse this situation.  She wants him to clean his face (and comb his hair) so that he will be presentable and look like someone who can be respected.  If he does this, perhaps he can learn to respect himself as well.
In this story, Roger’s face symbolizes the state of his life and his self-respect.  Mrs. Jones wants him to wash it as a first step to regaining his sense of self-worth so that he can stay out of trouble.