You say he has been living with you - so he moved in, perhaps to save money because of course he could not go on living with the wife and kids. So now, because you gave him a roof over his head, you want to delete his past. You cannot. But of course, you can check to see which pictures are being put on social sites, and say "How weird!" about the ones, and only those, to make your point, where he and the ex are alone and snuggling up. You are not being unreasonable about these - but, no, about the others, I'd not make a production out of it.