Thank you for playing and taking the time to leave a comment! I'm glad you enjoyed the demo :)
Oh, I probably didn't make it clear in the tutorial, so it's my oversight. If there's no outstanding choices to be made in the PMs, there should be a tiny X that shows up at the top right corner of the chat tab next to the character's name! If you close all of the open PM tabs, the whole PM chat window would close.
Sorry about that! I should probably add a note for it somewhere in the tutorials, haha.