So, this is my first post, but I do know quite a bit about endocrinology. In my opinion, there isn't a whole lot of reason to take T4. It can convert to T3 or rT3. If you're using T4/T3 to cut, rT3 will be counter-produtive. Also, with a longer half-life, T4 is harder to control. Further, unless you have a damaged thyroid or iodine deficiency, your T4 is fine. The important factor is whether or not your body is converting it to T3 or rT3. Most of thyroids effects that are useful in bodybuilding are mediated by T3 since T3 is waaaay more powerful.
As far as recovery, assuming that you were actually taking a blend of T4 and T3, you should find that your thyroid recovers once the compounds clear + 1-2 weeks at the most. People have taken thyroid meds for years and gone off and had there thyroid fully recover within 2 weeks. It isn't like anabolics, LH and FSH.
What will likely happen in your case is that the T4 will mostly convert to rT3 to balance out the T3 and much of the T3 will be protein-bound (inactivated). The half life of T3 is only a few days, so once this wears off, you'll probably have a reaction that is the opposite of T3, in other words, you'll be hypothyroid-like, but that should clear pretty quickly. The T4 that you have has a longer half-life, but it doesn't do much on its own and your thyroid will essentially wait for the T4 to fall to a more reasonable level then gradually ramp up its own production to keep the T4 at the right level after that.
All in all, use a good source for these things, but assuming you did, you'll probably be fine in under 2 weeks, very likely much sooner.
Best. And, be safe people.