Search Results: guys with girlfriends still flirting

Ok so me and my boyfriend been together for 6 months. He treats me right and all. he's quite an open guy so he tells me stuff like if a girl tries to call him, text him or message him on fb. So anyway, he has told me about his past (his exes and past flings).
there's this girl that he used to have a fling with and she still messages him few times. She would always message him "hey" at 4am. He would respond "hey" back to her but would just exchange few messages (nothing flirty). So today, she messaged him again saying "hey" at 4am again today, and he replied "hey, dont think you should message me again because i got a girlfriend now and im serious with her" and he also showed me all their other messages from last year. She flirts with him (e. g. she asked him to hang out) but he doesn't flirt back and just talk to her as a normal friend. Like when she asked him to hang out, my boyfriend would reply "i dont know I've been busy but ill let you know"
Should I be worried? Should I do anything about it? Why would she text him 4am all the time? So annoyed