SO has framed photo of him and ex? *UPDATED*

OK so my SO and i had a conversation recently in which he said he gets rid of all photos of him and exes because he finds it awkward to keep them. However there is a framed photo of him and his ex in the top drawer of his desk, faced down so you can't see the picture without flipping it over. (we met when they were together and started dating a couple months after they broke up and have been together almost 6 months).I effectively live with him so I know he never looks at it but still. I'm a bit insecure when it comes to his ex because she keeps messaging him whenever she needs someone to talk to, often until 1-2am at night, and she often turns the conversation onto their break up. He's told me he feels weird having an ex he doesn't hate, and I've told him that although I'm not uncomfortable with them talking so much, I'm not going to control who he talks to, and to be fair he's spoken to her way less since that conversation. Anyway, my question is how would you feel if your SO kept a framed picture of them and their ex? Am I overreacting because I'm sensitive to this subject?

UPDATE: OK, I sat down and asked him about it and some other questions. He said he doesn't feel right throwing it out, which I can understand, I'm a sentimental person too and I wouldn't feel right him throwing it out anyway. He said it was face down so that way he didn't have to see it and it wouldnt make him sad, which made me ask does he miss her? He said no, he has me now. I asked if he regretted meeting me (because we met before they broke up) and he said no, he loves me and he's happy with me. I asked if he had enough time after his break up to get over it, and he said he didn't know, that he regrets all the hurt that surrounds their break up and that's what still upsets him the most. I asked if he wished they were still together, he said no because he loves me, but then added 'Girls will only lower their standards once for a guy' meaning she wouldn't take him back anyway (which I disagree with because of her behaviour but that's another story) but him saying that got to me. I apologized for bringing this up because I know it upsets him, but he said it's OK because its important, and admitted sometimes he thinks about things like this too. I don't really know how to take all of this, obviously I'm thrilled to hear he is determined to stay with me, but I'm worried he hasn't moved on properly, obviously he wants a future with me but his past is still affecting him. I don't really know what to do but we're both going away for a couple of weeks to see our families so I hope having some time apart will help me figure things out. Thanks for your advice ladies, it's really nice to be able to hear someone else's view rather than driving myself crazy!