I think the concept they’re testing is the increased TBG levels in pregnancy, and not just hyperthyroidism in general.
When screening for hypo/hyperthyroidism, TSH levels are ALWAYS preferentially checked because they are more sensitive to minute differences in T3/T4. Often times TSH levels can demonstrate a change even when T3/T4 levels are in the subclinical range. The only exception to this would be in pregnancy (and I guess maybe liver failure? I doubt they would ask this though). High estrogen levels prevents the liver from breaking down TBG, leading to increased TBG levels in the serum. This binds to free T4, decreasing the amount of available free T4. As a compensatory mechanism, TSH levels are transiently increased and the RATE of T4 production is increased to replenish baseline free T4 levels. However the TOTAL amount of T4 is increased.
The question is asking how to confirm hyperthyroidism in a pregnant woman --> you need to check FREE T4 levels (because they should be normal due to compensatory response). You cannot check TSH (usually elevated in pregnancy to compensate for increased TBG), and you cannot check total T4 levels (will be increased). You got the answer right either way but I think this is a different reasoning worth considering, because they can ask this concept in other contexts of hyper-estrogenism, and if they listed “TSH” as an answer choice that would be incorrect.
Hypo/hyperthyroidism is diagnosed with TSH w/ reflex to T4 (this just tells the lab if TSH is normal don’t check T4 but if TSH is abnormal, check T4 too). TSH wasn’t an option so T4 is the best answer.