There are different motivations behind Mrs. Jones taking the boy home with her.
Langston Hughes is such a great writer because he presents deep characters. They are complex, and possess psychological layers within them. Like most human beings, their answers are not simple. Mrs. Jones is one of these characters. She recognizes that Roger experiences neglect in his own life:
“Um-hum! And your face is dirty. I got a great mind to wash your face for you. Ain’t you got nobody home to tell you to wash your face?”
“No’m,” said the boy.
“Then it will get washed this evening,” said the large woman starting up the street, dragging the frightened boy behind her.
One of the reasons she takes the boy home is because he has no one to take care of him. She assumes the role of leadership.
The idea of neglect continues when Roger says "There's nobody home at my house." The act of communion in preparing dinner for both of them reveals more of their stories. Mrs. Jones makes this clear to Roger when she says, "I have done things, too, which I would not tell you, son—neither tell God, if he didn’t already know." This confession reveals one of the motivations she had in bringing Roger home with her. She wanted to help him avoid some of the errors in judgment that she committed when she was younger. Seeing Roger attempt to steal her pocketbook was one such error. She saw an error that he was making that mirrored something in her own past. In seeking to make right that which is wrong and acknowledging her own flawed condition as a younger person, Mrs. Jones is motivated to take Roger home with her.