Medication for life
To medically manage hyperthyroidism your cat will need to receive a medication called methimazole (Tapazole or Felimazole are two brand names commonly used) every day (typically twice daily) for the rest of their lives.
methimazole blocks thyroid hormone secretion but the tumor continues to grow.
Numerous side-effects such as vomiting, loss of appetite, severe facial itching, liver damage, drop in blood cell production and an increased susceptibility to infection make this treatment option less than ideal for long term therapy.
Drug resistance (due to continued tumor growth), numerous side-effects mentioned avove, difficulty of pilling a cat, the long term cost of medication and periodic lab testing for the rest of your cat's life need to be considered when making your decision.