Would you be upset?

***UPDATE*** 
So I decided to just talk to him when he got home, and it went well. He said he did delete messages for space, and showed me some that were wiped clean that very same day. The ones I saw he purposely kept because he needed info on them. I didn't look through his whole phone, just the people he'd been texting recently. I believe him, and everything is fine, but dammit I hate these preggo hormones that make me so damn sensitive. Thank you for all your productive suggestions, I was impressed that only two people obviously can't read. 🙄 
My husband texts people from work often, and one of the girls is way too flirty. He has always told me things she says etc. However he is bad about not telling me details & just prefers to hand his phone over for me to read for myself. (He does this with lengthy texts from anyone that he wants me to read, not just this coworker) About 6 months ago, he was telling me something she had said, but didn't give me the phone. So I looked myself and the entire convo was deleted. I asked why and he said he didn't want those things on his phone. (He's an officer in the Air Force and she is enlisted. They could both get in trouble for anything inappropriate) I told him I was not cool with that & if its something that could get them in trouble it certainly didn't need to be said in the first place. I also told him it was disrespectful and I would not be tolerating crap like that. He agreed and supposedly had a talk with her. Well I was looking at texts for another reason (he knows I was doing this) and decided to click on the ones between she and him because they both had to work a special event recently so I was curious. Well, he deleted the history and all I could see was Saturday after I was about to show up to the event. (Pic posted, last msg from her said "oh ok, that's cute.") So now I am contemplating pulling up all the deleted texts. I know how to do this with software. Spare me the "you shouldn't snoop, if you don't trust him don't be with him" comments. I trust that husband hasn't done anything physical, and we have a great marriage, but I'm not stupid and if there are little flirtations then I want to know about it, because affairs don't start in the bedroom. She starts the convo here, and the blurred out name at the end in blue is my name. Everything prior to this first msg at 11:57 has been deleted, and he did not clear any other conversations that day, so I know it wasn't for storage space. How would you feel about this situation? What are your thoughts? Again, don't bother if you're just going to judge/criticize the trust or the fact that I looked at their messages.