Iodine and low thyroid (hypothyroidism)

At my last annual blood tests they found my TSH levels were high pointing to an underactive thyroid. My PCP put me on sythroid with a followup in September but he is retiring so I took it to my endocrinologist and she warned me about taking centrum silver because of the additional iodine. Anybody on thyroid meds get those instructions??

Dr. Google seems a little mixed on the subject. Sometimes you need iodine and sometimes extra iodine can hurt. Any thoughts on the matter?