Boyfriend texting this girl, should I worry?

My boyfriend and I have been together for almost 4 years, we've been living together for the past year.We have no problems living together, or no problems in general except my insecurities.

I'm so insecure and jealous because it's a problem I have within myself that I need to work on.

My boyfriend is very honest now. (he did cheat in the past but we broke up because he felt he needed to get his life together.) now that his life is together, has a job, bought an apartment, back in school, he's completely different. the way he talks to people, his whole persona is new and improved.

now he if he goes out with the guys he'll come home and tell me about how he saw an ex-girlfriend there, or how a girl he had sex with in the past tried talking to him. he's very honest about stuff about other women without me asking. (like the examples shown above)

Last night he was texting. I was curious to see who it was after he had stopped texting (my insecurities make me curious)

he hande me his phone so I could order pizza,

before I dialed the number I looked at his texts and he was texting a girl. this is the conversation:

boyfriend: what time are you off tonight

girl: I'm already off! I got off early because they had a cancellation :/

boyfriend: oh sh*t are you still trying to go out tonight

girl: I'm already in bed! and it's so cold! but we do need to kick it

boyfriend: ha ha OK just hit me up when your free

girl: will do! have a good night :)

-my boyfriend didn't reply after that-

I mean, he left it in his inbox and didn't immediately delete the conversation,

and he knows I look through his phone here and there but doesn't mind because he says he has nothing to hide. this morning I was texting and he asked me "oh who are you texting" because I smiled when I received a text and I said "no one I don't ask you who you're texting" then he said

"you can go through my phone right now and look it, it's all out there in the open for you."

last night he went out with his friends and when he got home and went to bed I checked his phone and he still had not deleted that conversation with that girl. and he was texting me while he was out so I know he saw he still had her in his inbox.

should I worry over his text with this girl and how he hit her up to hangout?

or am I being crazy? he hasn't deleted the conversation, and I would think he would delete it knowing how jealous I get and that I would start a fight over it...

I am going to talk to him about it, but I just want some opinions on the situation before I do

thank you for your time