Race isn't just a peripheral theme in the story; in many ways, it serves to characterize the grandmother and to illustrate her hypocrisy. The grandmother believes herself to be both a fine lady and a good Christian. When facing her impending execution, the grandmother wants the Misfit to turn to God, telling him that he's a "good man" who only needs to pray to Jesus for help. Her "Christian" efforts to save the Misfit are a veiled effort to save herself, and he sees through her empty words, telling her, "I don’t want no hep...I’m doing all right by myself.”
Her misguided understanding of Christianity is also reflected in her racist comments earlier in the story:
"Oh look at the cute little pickaninny!” she said and pointed to a Negro child standing in the door of a shack. “Wouldn’t that make a picture, now?”
And then later:
“Little niggers in the country don’t have things like we do."
In her comments is no sense of Christian compassion or charity. There is no sense of loving others or of helping those in need, which are fundamental beliefs of Christianity. Instead, the grandmother views herself as racially superior to these unfortunate children whom she views with detached amusement from her car window.
Thus, we realize that the salvation which the grandmother offers to the Misfit is a reflection of her own spiritual needs. Her racist heart highlights the fact that she is neither a "lady" nor a Christian, and the reader thus feels less sympathetic towards her eventual death.