You might go with the following:
In Flannery O'Connor's "A Good Man Is Hard to Find," the grandmother's conception of morality has a great deal more to do with whether or not one agrees with her than it does with actual goodness.
In order to prove this, you could discuss her interactions with Red Sammy. When the grandmother's family stops to eat, she and Red Sammy bond over their shared laments that "'These days you don't know who to trust'" and that "'People are certainly not nice like they used to be.'" Although Red Sammy is dirty, keeps a monkey chained to a tree, and treats his wife poorly, the grandmother feels a connection with him. He is not a good man, even though the grandmother says he is; it's simply that his values and hers are the same.
The grandmother herself discusses "better times" when "'People did right [...],'" though she lies freely to her son and his family in order to get what she wants. She is embarrassed by the sassy behavior of her grandchildren, but she uses the n-word and talks about the Old South and plantation life as though it were a better time. She is not a good woman; her values are old-fashioned at best, racist and elitist at worst. She is precisely the kind of person responsible for the Misfit's terrible fate.
Therefore, when the family has an accident and the Misfit and his friends stop, the grandmother's behavior toward him actually has the opposite effect than the one she hopes it will because his values do not match hers. She tries to assure him, saying, "'I just know you're a good man [...]. You're not a bit common.'" However, he tells her that he isn't a good man, that he went to prison for killing his father, a crime he didn't actually commit. He eventually realized that it doesn't matter what crime one commits; "'sooner or later you're going to forget what it was you done and just be punished for it.'" As a result, he thinks that one might as well do bad, if one is going to be punished whether one does bad or not: "'No pleasure but meanness,'" he says. The Misfit sees the disconnect between the grandmother's values and his own. He's been mistreated and condemned, his life ruined, probably by elitist individuals like herself, and now she's trying to manipulate him by making it seem as though they have some values in common.
In the end, he recognizes what she never could, that she was not a good woman, at least, not until the very end of her life when she tried to reach out to him in a legitimate and loving way. He says, "'She would of been a good woman [...] if it had been somebody there to shoot her every minute of her life.'" In other words, it was only the threat of death that compelled her to see the real connection between the Misfit and herself, the connection between two human beings—not a connection between social equals because, ultimately, one's social status isn't a factor in calculating one's goodness.