My boyfriend still talks to his ex??

So I recently started dating this guy we have now been together for a month and a half. And I noticed one day he got a text from his ex (If you guys are wondering he’s 21 and I’m 19). Now, long story short I told him I’m not comfortable with them still talking and he said “I told her not to text me anymore so it shouldn’t be a problem”. He has her blocked on every social media but he won’t block her number. I talked to him about it today cause I noticed that she was still texting him. I told him again that I am very uncomfortable with it and it irritates me. It irritates me because they dated for two years and they somewhat ended on good terms. he told me he doesn’t want to lose her as a friend but I think he needs to get over that and block her. I will never be okay with them just being friends and I told him that too. I just need advice.. Am I over reacting or she he block her?