I think what your doctor meant was that you tested negative for antibodies, i.e. you had none, or the count was low enough to fall within normal range. That's a good sign. It shows that you have no left over thyroid tissue in your body. Your antibodies have gone down because they no longer have anything to "fight" now that your thyroid has been removed. It often takes a while after surgery for the antibodies to disappear. Sounds like good news to me!
Did you have the antibodies before your TT? I also have the antibodies, and had them prior to surgery. I think the idea is that the antibodies can mask the amount of Tg in your blood. So usually, they watch the number of antibodies along with your Tg . . .if the antibodies go up, even if the Tg stays down, that is worrisome. along as they are stable of decreasing, I think thats ok.
if someone else has more info, please post.