is he over his ex?

Ivanna
Soo I met this guy on a dating app back in February and we really hit it off. I really liked him and he said he really liked me, but then I found out after a month (we've only been talking) that he had only just broken up with his ex of two years a week before we started talking. 
We had had a long conversation about his ex, where I told him I didn't want to be caught in the middle of something or be the rebound, and he really tried his best to convince me that he was over her. I told him I needed time to think it over and he did. After a bit of time, i was convinced so we started talking again. Especially since she got a new boyfriend and he stopped mentioning her as much.
So now we're actually officially seeing each other, but I'm confused because he still mentions her sometimes if he has a story with her that matches what we're talking about. And he still keeps a gift she gave him for his birthday (after the breakup) on his keychain. The thing is, he doesn't have many friends and she was obviously a close one. 
So should I be worried and bring it up with him again or should I let it go as them being friends?
He's never given me any reason not to trust him so I don't want to look for one. 

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