I've never heard of this and I'm very curious. Is it anything like the staring nonemotive visage associated with Parkinson's?
Typically Graves patients are very animated and in motion. Since thyroid hormone controls the level of metabolic activity, they are jazzed up.
If untreated and undetected, Graves disease can cause one’s eyes to permanently bulge in a bug-eyed manner, ergo my Marty Feldman reference (he was a sufferer of this). Barbara Bush looks to have acquired a bit of this from her bout with the same.