This paper shows that TSH and FT4 in blood does not reflect urinary iodine levels. This indicates the thyroid is flexible to iodine supply and is robust to limited iodine in diet.
Do Thyroxine and Thyroid-Stimulating Hormone Levels Reflect Urinary Iodine Concentrations
Soldin OP, Tractenberg RE, Pezzullo JC. Ther Drug Monit.
2005 Apr; 27(2):178-85. PMID:15795649