My SO and his ex, need advice long sorry

Cheyanne • ♠♎♠
Soo I've been with my SO for about 3 months now and we live together, which seems kinda fast rolling, but we just clicked and went with it cus fuck it, life's too short lol Anyways I was texting someone back for him on his phone and noticed his ex, I'll call them J, who was actually his fiance at one point, but toyed with his heart and took it back. Well anyways I'm not really a jealous person at all and I could really care less if he's texting her cus she's part of a fairly close knit group of friends that he still associates himself with. Well moral of the story is, he's told me stories about this woman of how he would try and move on and as soon as things seemed to be getting better she would would start talking to him again and start basically telling him all the warm nd mushy stuff girls tell guys when they care about them. Well anyways I'm not worried about him seeing his responses were very clear that he didn't want to even be just friends as she suggested, but I'm still kinda bothered should I be?