Assuming you are an adult and your T did not have permission to communicate with the family members in this situation.....this would upset me a lot.

I would definitely bring this up with T in the next session. For your T to respond to that e-mail by saying "thanks".....your T confirmed that you are a client which by itself violates confidentiality. This would be a HUGE "no-no" for me. My problem in this situation would be the fact that the T chose to acknowledge to this family member that I am a client. I would also let the T know that in the future, if something like this occurs, I would expect to find this out from T rather than on my own.

P.S. As mentioned already, this is exactly why I don't tell ANYONE except my husband that I see a T.....let alone share the T's identity!