I've never heard of suck a thing.
I am on 50mcg ED of T3, my thyroid died a few years ago. I have done low carb diets for months at a time since then and I have not noticed any problems. I do take this ED due to a medical condition so I am not sure if low carbs with T3 in a healthy person will cause permanent damage to the thyroid.
IMO T3 should not be used unless you are a pro looking for an edge. The thyroid is a very sensitive gland and it doesn't take much to hurt it. A sizable percentage of people who use T3 for weight loss purposes end up permanently hurting their thyroid.
Since my thyroid went down I have been on T3. My life was a living hell when my thyroid died. Depression, cold feet, eating 1200 calories ED and not losing weight. Even now my thyroid levels come in good when I get my annual physical done but it is hard as hell to lose weight and getting down to 7% is very, very difficult. IMO there are safer ways to lose weight.