Shady phone stuff

I just found out that my boyfriend still talks to a girl he used to mess with. He face times her and calls her then deletes the evidence. I called him out on it and he states that he’ll never hurt me again. However I can’t seem to get over the mistrust. I am completely open with him. He has access to my phone, I tell him who I e had lunch with who I’ve gone out with. I’m a completely hurt because when we meet he was the sweetest person and I would have never thought he was shady like this. Now I’m torn should I try to make it work and have this on the back of my mind or cut my losses and move on. I do love him but this hurts because I trusted him so much.