Hello and welcome!
Rituximab is considered an experimental therapy for TED. One study overseas showed great results, but another study in the U.S. did not show improvement. Researchers are still trying to figure out the reason for the differing results, although the U.S. group was in general older, had higher antibody levels, and did not get diagnosed as quickly.
There are cases where patients with Hashimoto's thyroiditis (which causes hypothyroidism) end up getting diagnosed with Graves' disease years later. In other cases, patients with Graves' disease can end up flipping hypo.
In terms of deciding whether the disease is stable, some doctors rely on antibody tests (like TSI), but in most cases, doctors will rely on whether your double vision is improving, worsening, or stable. Doctors like to see a few months of stability before doing surgery, as they don't want to put you through a second surgery if the eyes change again.
TSH is a substance produced by the pituitary gland that either directs the thyroid gland to produce more hormone or to put the brakes on thyroid hormone production. The amount of TSH produced generally depends on a “feedback loop” according to where our thyroid hormone levels (T3 and T4) are. When T3/T4 are too high (hypER) the pituitary shuts down production of TSH to try and tell the thyroid to stop producing extra hormone. When T3/T4 are too low (hypO) the pituitary cranks out TSH to get the thyroid to produce MORE thyroid hormone. (With Graves’, the feedback loop can be interrupted, with TSH staying suppressed, even though T3/T4 are in the “normal” range.) Although thyroid eye disease can occur at any time - even with no thyroid dysfunction or years after treatment - being hyper or hypo does increase the risk of eye issues. So this is why your doctor is running blood tests - and hopefully he/she is working with you on getting your levels balanced.
You might be interested in checking out the GDATF's videos on YouTube, as there is a lot of great information on thyroid eye disease presented by experts in the field:(Note on links: if you click directly on the following link, you will need to use your browser's “back” button to return to the boards after viewing, or you will have to log back in to the forum. As an alternative, you can right-click the link and open it in a new tab or new window).https://www.youtube.com/user/GravesAndThyroid/videos
You might also check out the “Men With Graves' and TED” thread towards the top of the forum.