Would you be ok with it?

So my fiancé is a manager of a gas station. Occasionally people will leave personal items at his store. I have found out that he will private message them on Facebook letting them know that he has it at the store. I didn't think anything of it, until a girl left her phone in the store about a month ago. She picked her phone up the other day and left a baby outfit for our daughter. I didn't think much of it right away, but eventually I started thinking about it. He has had numerous conversations with this women other then letting her know about her phone. He doesn't know her name supposedly but he thought it was acceptable to message her letting her know the gender of our child. Is it wrong of me to be upset about this? He says that he didn't do anything besides talk to her about him and I and our baby on the way.