My Work Buddy

So rencently I started talking to this guy I work with. I know what your thinking a BIG No No !, but I can't stop that we are Pysical attracted to one another. So we've been talking & hanging outside of work . He's a gentleman and every way. We just had sex and he's a bit on the smaller side but the sex is okay. My only issue with him is his ex. Every time I'm at his house she pops up ! I mean every time!! So when she first popped up , I was like oh. She's an ex and  Apparently not over him . He explained that the young lady lives right down the street & I was understanding at first but now I'm like okay what's the real issue. I know we are just talking but I like him . I've brought how I feel up a couple of times but don't want to nag him about only because we aren't a couple . He reassures me and then brushes it under the rug like it never happened. But I've seen his phone & she still texts him & I have his password. But he doesn't know . My question is do I snoop while his sleep or just let it be ???