I wouldn't have a problem with my T googling me once or twice, but clearly it bothers you a lot and that's a valid position to take. I wondered also, what LonesomeTonight and ArielAwhile mentioned, if she was trying to figure out ethnicity or something like that—that seems a bit offensive, honestly, and far more personal than, say, your hometown or something. If this T has been helpful otherwise up to this point, I think you could try to go forward but with the understanding that you need to control what information she has about you and that she will not look you up like that again. Even if it is okay with some people, it is not okay with you, and that is important for her to understand and acknowledge.