Boyfriend talked to ex girlfriend for weeks behind my back

Hi!

So for context my boyfriend is 23 and I’m 20 and we have been together for two years and have lived together for a year and a half.

So, a week ago my boyfriend was reminiscing about an ex girlfriend he had 4 years ago.

He was talking about their relationship and how they had started off as “best friends” for about a year before they dated and how his other ex believed he cheated on her which he adamantly denied, but did admit they began dating very soon after his ex broke up with him.

While talking about her he mentioned that she still texts him every few months to try and get back together and mentioned that they had been texting back and forth a few weeks ago that he never told me about.

He said that he only responded to “be polite” however, he replied to her for about three weeks…daily… he said she stopped texting when he mentioned he had a girlfriend…3 weeks into their texting spree…

I haven’t brought it up since that conversation however it has been bothering me a lot. Especially since he brings her up every chance he gets (I.e. telling me stories about her whenever the opportunity presents itself).

Is this a petty thing to bring up to him? I trust him 100% even though he doesn’t always share everything with me :/