In agreement with the other post: (see FA2020 p331)
You would want to check FREE T4 because pregnancy increases Thyroid binding globulin. It is possible she might have increased overall T4, but NOT have hyperthyroidism because the free T4 is normal (i.e. her increases amount of thyroid binding globulin has bound more T4, and since our bodies respond to the concentration of free T4 only, the hypothalamus should ensure that the free T4 is kept constant; this would appear as increased overall T4)
Another way of thinking of this:
If we increase bound T4 and keep free T4 the same, we would still increase overall T4. Thus to know if she truly has hyperthyroidism we must look at free T4 concentration.
Estrogen increases Thyroid Binding Globulin (TBG). (FA2020 - 331).
TBG binds free T4 --> increased total T4 and decreases free T4.
TSH rises to compensate for decreased free T4 to return to normal states.
Therefore in pregnancy total T4 is increased but free T4 is normal. If T4 were to be increased --> hyperthyroidism.