Personally, I don't think searching your T on the internet is a big deal. I know that it feels weird, especially if you end up finding stuff like the value of their house, etc. but if it's in the public domain, and knowing that stuff isn't going to interfere in the work you're doing in therapy, I don't see the problem. I almost see knowing something about your T as evening out the playing field a bit - they know all about you and you don't know anything about them (I don't know about you, but I'm genuinely curious about my T).

The one thing that I have noticed though (that is problematic) when people find information about their T online is when it leads the client to compare themselves to the T. For example, I've read posts in which people have begun to feel badly about their own living situation after discovering that their T lives in a wealthy neighborhood in a home which the client couldn't afford. Comparisons like that may be worth mentioning in session, because it could be a representation of a larger issue to work on in therapy.