If your wife knows about it, you are transparent and she doesn't mind, I don't think it is anyone else's business. Just be honest with yourself. If her contact gives you excitement, it's probably better not to carry on the communication. Otherwise, enjoy it for what it is.
My best friend from school is an ex boyfriend but the reason he's an ex was because as much as I liked him as a person, I didn't fancy him enough for a life long relationship. My husband, in the past a jealous soul, is not the least bothered. He gave me away when we married and he was the Godfather of my child.