Hi Stacie,
I guess there could be many reasons for this. This behavior is called "pica" and can happen when young kittens were removed from their mother before they should be.
Your kit is 10, so I am thinking it is somehow related to the Thyroid imbalance, meds, or the new food.
Talk to your vet and see if this behavior could be related
Stress, seeking attention, and some other medical problem could also be causing this. Best to have some blood work done on the little guy.
Perhaps others have some other ideas and will chime in.
Keep us posted.
CML
Just be sure Kit can "Lick but not swallow The new menu" that could cause an intestinal blockage.
Miss Hildiekatt likes to lick the straps of those reusable poly fabric grocery totes. This behavior started after the move from Illinois, so I think its a comfort to her, no harm being done. Likely smells Anita and me on the handles.
I agree w/ CML that since this is a new behavior for your kitty, this is more than likely due to being hyperthyroid. He's trying to get something his body senses that he is missing to make up for the imbalance.
Pip, I agree w/ you that Hildie is probably licking to make herself feel secure with her move to MD.