If he were decent, he'd stop lying to his granny and just say "no she's not my girlfriend" or at least say "we broke up". And even though there was an agreement of mutual uninvolvement, the first thing he does when he sees that she lives next door to him is try to pester her, even though she clearly doesn't want anything to do with him anymore. Perhaps a good restraining order is what's needed, since the guy has no self-control, and cannot take a hint.
The author repeatedly inserts contrived circumstances in order to keep them attached and stuck together, like how "oh, they happened lived next door to each other all along, haha!" Seriously? What an ass-pull! I want to give this manga a chance, because I do like comedies, and I did laugh at a few parts, and I'd also kind of like to see some of the general themes explored a bit more; But I think this author lacks the ability to carry the story forward in an effective, convincing, and original way, or at least in a way that doesn't rely on trotting out one hackneyed cliché after another. I might try until chapter 5 or 6 until I give up on it, and just hope that it somehow gets better, or more interesting, or at least tones down the odiousness of the male MC. No idea if it will get any better, but I guess I'll find out.