I don't know why this is in the chemistry forum, but anway...
It's not quite "Reverse T3," but when you carb deplete you also decrease t4 to t3 conversion in the liver, which then leads to decreased metabolism. You still lose fat on keto diets though because they work through other mechanisms, mainly lowered plasma insulin levels and inefficiency in using ketones for fuel. The lowered t4 to t3 conversion can be remedied with taurine and a little fructose in the diet.