Iodine is normally used to slow down thyroid hormone production in hyperthyroid with humans. Is the 7 TSH? If so, that is not an accurate measure of thyroid, but of pituitary. Iodine leaves the body within 24-48 hours, so if u stopped the iodine, the symptoms should subside unless the cat has a hot nodule or cancer. I don't know if u can supplement a cat with selenium, tyrosine or l-carnithine, but maybe someone else would jump in.

http://www.uptodate.com/contents/iodine-in-the-treatment-of-hyperthyroidism


What Are the Symptoms of Hyperthyroidism?

Weight loss and increased appetite are among the most common clinical signs of this condition. Weight loss is seen in 95 to 98 percent of hyperthyroid cats, and a hearty appetite in 67 to 81 percent. Excessive thirst, increased urination, hyperactivity, unkempt appearance, panting, diarrhea and increased shedding have also been reported. Vomiting is seen in about 50 percent of affected cats. Clinical signs are a result of the effect of increased T4 levels on various organ systems.
http://pets.webmd.com/cats/guide/cat-hyperthyroidism

Dr Jeffrey Dach on hot nodules

http://jeffreydach.com/2011/09/06/iodine-induce.aspx

IMO, If I had a hot nodule, I would get my D levels into optimum and get plenty of selenium, tyrosine and carnitine, but for an animal, D levels are hard to figure out because vets don't test for it. I wonder if u tested a cat's D levels using ZRT lab's 25 hydroxy D test would give the same results as with humans?