Harry,
Until Carol came into his selfish lonely life, Melvin behaved like a spoiled child who was only concerned about what others could do for him. Carol had one goal in mind, to do all she could to help her sick son get well. It is no wonder that she was repulsed by Melvin's obnoxious holier  than thou persona.
At first he was only concerned about her desperate situation because he wanted her to continue serving his  demands. Her distrust of his selfish motives eventually convinced him that she was truly a caring loving person who could not be bought off with money unless he radically changed. She made him feel like a "better  person" when ever he was around her.
Carol made Melvin a better person, you know like a good liberal tries to make selfish greedy conservatives less concerned about themselves and more concerned about others, similar to Jesus.