On the surface from what you have wrote, it sounds pretty innocent. I also think it's normal for you to be curious of what the intent of their contact really is.
I would continue to trust that it is nothing, let him be open to you about their relationship.
If he starts to hides things or you sense things are going too far, red flags start arising, shut it down.
If anything does happen behind your back, if he cheats with this woman, then you know hes not worth your time. It can only go as far as he let's it.