Great to see you!
I’ve not seen research on gluten intolerance and absorption, but there *have* been studies on celiac and poor absorption of levothyroxine:
http://www.thyroid.org/wp-content/uploads/2012/07/clinthy_v243_4_5.pdf
One question you might ask your doctor is if there is any concern that you have celiac. If so, your doc might want you to wait on going gluten free until after you’ve gone through testing (as that can affect the results).
Take care!