Maybe you could tell the vet that i.e cat kibbles are fortified with several MG of Iodine per kilo. There is probably a reason for that:)
I believe the one I give my cat (Canagan, grain free) has somewhere between 3-5 mg per kilo, depending on which kind of "flavor"
I have fortified my cat`s water with Iodine for 7 years now (with pauses now and again)
- the one I have now is very active with a great personality; but the food is crucial. Some raw liver, meat, fish + good kibbles.
He gets a tick bite now and then, which I treat with Lugols too, all together I believe he gets at approx a milligram per day.
Once a month I give him 50 mcg of selenium. In the water I also put a drop or two of magnesium oil.