Since TRH responds to a low freeT3, does TSH itself also respond to a low T3 (total and/or free)?

The hypothalamus responds to levels of thyroid hormone in the blood via the classic biofeedback loop and releases TRH in response. Basically, high thyroid hormone levels suppress TRH (High T3 is the strongest inhibitor of TRH). Low hormone levels increase the production of TRH (Low T4 levels are the biggest stimulant of TRH).

There is evidence that TSH output from the anterior pituitary may be directly inhibited by high levels of circulating T4. However, the hypothalamic feedback loop is by far the most important and active biofeedback loop.