Hi Laura and welcome!

I have the opposite thyroid problem (not enough), but I found this on the web about Grave's:

"In some cases, surgery to remove all or part of the thyroid (thyroidectomy) is needed. Surgery can also relieve some of the symptoms of Grave's disease. Bulging eyes, for example, can be corrected by creating enough extra space in the nearby sinus cavity to allow the eye to settle into a more normal position."

http://www.healthsquare.com/mc/fgmc9032.htm