Girlfriend still talking to her ex on occasion?

Ok so me and my gf just started going out. she claims that her ex kept texting her about who she was going with since she put In relatiopnship on facebook. i told her to ignore that and that he should not be texting her . she agreed and ignored them . But then randomly she told me that she talked to him on the phone yesterday about me . I was just like ok, but that she knows how i feel about him sticking around.

I find his presence unhealthy and as if he is trying to make her feel guilty or bad and take advantage of her weaknesses for sex favors . she said she would not give in to that and i trust her but im not comfortable with knowing that he still has this obsession to message her and that she has not told him to **** off . what should i do ?