There is an approach that was promoted by some "gurus" that advocates on using T4 (and not T3) with GH. The notion here is that GH usage lowers T4 levels, which indeed it does, how ever GH also increases the T4 conversion into T3, T3 is the much more potent and active form of T4. So in reality the T4 levels do drop with GH usage, how ever the T3 may actually increase (this also explains partially the metabolic effects of GH).
So to summarize there is absolutely no need to take T3 automatically with GH, unless it's done purposely to further enhance fat loss.
GH does have some impact on the thyroid function, so I suggest to check the TSH and T4 levels, and if they drop below the minimal line to consult and consider taking T4.
Also consider - the GH impact on the thyroid is completely reversal and with stopping the GH usage the thyroid will get back to its normals