I have not encountered my T outside the office, so I don't REALLY know how I would react. However, I really don't think it would be a big deal for me. I'd probably just wave or give a nod. If it was a situation where introductions were called for I would probably just introduce her by name and move on before the ..."Where do you know each other from?" question follow came up.

Don't get me wrong, I am curious about my T's personal life. But I get the fact that it's best left unknown to me. I'd respect her privacy because at the moment I want our interaction to continue and wouldn't want to risk messing it up.