Hello – If T3/T4 are normal, with a suppressed TSH, this is referred to as “subclinical hyperthyroidism”. With this issue, the process is usually “watch and wait” to see if this progresses to “overt” hyperthyroidism, unless the patient is symptomatic (which it sounds like you are not) or at risk for cardiac problems (which is more of a concern in the elderly).
TSH can remain suppressed for quite some time in Graves’ patients — but it can also be an early indicator of progression to “overt” hyperthyroidism, with high T3/T4. It sounds like your doctor is preferring to err on the side of caution and check frequently to see if T3/T4 are increasing, so that you can catch things early if that does happen.
You might also ask about antibody testing, as the latest medical guidance recommends testing TRAb prior to withdrawal of anti-thyroid drugs. It’s not a perfect correlation, but low antibody levels do have some predictive value in determining which patients will experience remission. (Many docs define “remission” as a period of one year with no meds and normal thyroid levels).
Take care!