So, could I google your web site, Flatfeet? You've got me curious.
Not being sarcastic, but I do like to visit professional web pages, on many topics from art, to horse farms, to where to buy unique car seat covers, etc.etc. Frankly, I think a therapist could learn a lot from someone's web site if it tells or shows a lot about them and their product. As Freud was always explaining, everything the client says, dreams, and does, has meaning.
And I agree with the others who posted, that Anything you put on the web is accessible to anybody. And if your site has several pages, the T might return numerous times. I don't think it's weird of T, but an effort to help you.
I have a professional art website (several actually) and wish my T would see them, especially the article I wrote about the meaning of dragons in mythology.