The Misfit recognizes the grandmother's failings quickly. He sees that she relates to the world rather indirectly, engaged in fantasy and looking at things at she thinks they should be instead of as they actually are.
We see this tendency in the grandmother's treatment of her son, in her semi-constant monologue of nostalgia, complaint and comparison.
The effect of this tendency is to distance the grandmother from people. She is not entirely present with her family and she is also clearly not compassionate or sympathetic toward them. The emotional distance between the grandmother and her family is defended with a series of prejudices, fixed outlooks and attitudes.
A lifetime of prejudicial attitudes is erased, however, at the end of the story when she realizes her helplessness and the fact that discriminatory views such as hers are related to monstrous behavior like the Mistfit's.
The Misfit is not sympathetic toward people either. He feels no remorse for his violent crimes. A systematic belief that he is "in the right" allows him to achieve a similar impersonal distance, like the grandmother, between himself and others.
With a gun pointed at her, the grandmother suddenly connects to the Misfit. She is suddenly very concerned for her son also. In this moment, she the distance is closed between herself and those around her. She is no longer protected by her prejudices and her nostalgia. She no longer lives in the state of abstraction that these ideas represent.
The Misfit rightly sees that the grandmother is engaged with reality in this moment, not abstracted from it. She faces herself, realizes that she loves her son, and suffers without turning away into criticism, comparison or nostalgia.