Boyfriend troubles. Please help!

So first of all, I completely adore my boyfriend and wouldn't trade him for the world. A bit of background, he lives with his grandparents and his grandma is his legal guardian. He dated this girl named Arron a while ago and now that he's dating me his grandma won't stop comparing me to her. She's always saying things like "Oh well Aaron did it this way." So far the comparisons have been mostly positive but it still really pisses me off to the point where I want to tell her to shut the hell up. I get that she was a part of his life but the past is the past and he's with me now. She gets mad over the littlest things (she called him a slut bag after she asked if he WANTED to go to town with her and he said no he had homework to do) so I don't know how to handle this. What should I do?