She went back because she cared.
And in MANY situations, change takes TIME. It is not fast and easy, especially not with racist individuals. That is not an area where you talk to a person once or twice and that other person has changed their life's course of history in a couple of weeks.
Deep, embedded racism (overt or covert) takes time and I'm proud of Rebecca trying for that amount of time. And who knows, that elderly woman may have had time to think on it since Rebecca's last visitation and 'MAYBE' started on the path of change. Maybe. But that's just my optimism and hope for the human race.