Why doesn't Mrs. Jones ask Roger about his home or parents in "Thank You, M'am?

Mrs. Jones does not ask Roger about his home life because doing so is superfluous; her powers of perception tell her all about Roger.

After Mrs. Jones foils Roger's attempt to steal her purse by muscling him to the ground with two or three passers-by noticing the physical conflict, Mrs. Jones asks if he will run if she frees him. When Roger replies that he will, she refuses to release him and examines him:

“Um-hum!...

Mrs. Jones does not ask Roger about his home life because doing so is superfluous; her powers of perception tell her all about Roger.

After Mrs. Jones foils Roger's attempt to steal her purse by muscling him to the ground with two or three passers-by noticing the physical conflict, Mrs. Jones asks if he will run if she frees him. When Roger replies that he will, she refuses to release him and examines him:

“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.

Further in the narrative after Mrs. Jones takes Roger home with her and asks if he is hungry, Roger reveals that there is no one at home where he lives. 

Her questions about his dirty face and if he is hungry added to Roger's revelation that his house is empty provide Mrs. Jones a wealth of information about Roger's home life. For, she can easily surmise from this information that his family is a broken one and Roger receives no supervision or loving care, both of which are extremely important. Her acts of Christian charity and love toward Roger make a profound impression upon him, and in his gratitude for her kindness in not reporting his crime "[T]he boy wanted to say something else other than “Thank you, m’am” to Mrs. Luella Bates Washington Jones...."