How would you take this ....

So my current bf has a child with his ex wife and I told him it bothers me when she texts you and I don't want her talking to you unless it has something to do with your kid. Not my thing is that I've noticed when we're not together. I'm sure she does text him and before he and I get together he erases the messages. I asked him why do you erase them and his response is because he doesn't care to have them. Sometimes I feel as if she wants to get back wth him and I should just walk away. And other days I feel I can trust him. She's told me countless times he doesn't love her and doesn't care to be with her at all ... but what bothers me the most is that she's gonna be apart of his life.... forever. And it annoys and bugs the shit out of me.