There has been talk of a connection in that area for many years. The tragedy is that many people still get auto-immune disease and are not eating wheat!
Personally I think you might find it coincidental that your TPOab's went up at the same time of having a gluten free diet. The anti-bodies in gluten can and do give rise to many similar symptoms to that of a person with thyroid disease, but the thyroid anti-bodies have nothing to do with gluten.
I am a gluten intolerant and have Hashimoto's disease. Even with being on a gluten free diet for many years I had no relief from any symptoms, which I believed where from gluten. I was then diagnosed with Hashimoto's.
It is very common for thyroid disease patients to also have gluten intolerance. But then many also have low Vit D also. It is an interesting connection and one I am sure in future generations of scientists will find an answer to.
The only thing I've consistently heard helps to reduce thyroid antibodies is selenium (I believe 200 mg per day, but don't rely on my memory for that!). However, there has never been any large-scale study to prove or disprove the selenium connection. I have read about a small study recently of an esoteric population in Greece which showed a connection. It had very few subjects. As with any other supplement, if you are deficient, it might make you feel better, if not, maybe not so much. However, many people swear by it.
Since Hashi's is an autoimmune disease, if you have one, you are more likely to have another like celiac disease (gluten intolerance). Antibodies are very specific to their antigen. Eliminating wheat intake will reduce the celiac antibodies, but has no effect on the thyroid antibodies. Perhaps, it's just the coincidental effect of "feeling a little bit better all around"?
I have a question. My labs came back with a reference range 15 H. What does that mean?
Just my advice, but many health professionals are beginning to make the connection between gluten, grain and soy products and immune system dysfunction. I believe that, in some people with thyroid problems, carefully attempting an elimination diet and seeing if it helps you is worth a shot. I'm on a Paleo diet that's been painfully customized over the last 6 months that includes some vitamin D and selenium supplementation that has done wonders for both my thyroid blood work and overall well-being. However, I would say every person is different and you have to figure out what works best for your physiology.