Unless I misinterpreted what you wrote, it did sound a bit like your tdoc was mocking the idea of bringing a pet to therapy. If you're unsure of that, or agree with my interpretation, you might consider telling them that you felt they mocked an idea that you were serious about. That may not get them to agree to you bringing your dog, but I think they need to know that their words were hurtful. If not to you, they sure might have been to someone else.

I have never brought a pet to a therapy or psychiatrist session. I don't currently have a pet, but have had a parrot for years in the past. I clearly remember, about two years ago, my psychiatrist saying that he has (or has had) patients bring their pet to sessions. I jokingly asked if I could bring my parrot, and he said "Yes" pretty seriously. I didn't bring my parrot because I didn't really need that, plus my parrot wouldn't have liked to go (and wasn't reliably potty trained). However, it was very sweet to know that my psychiatrist allowed that.