Hello, I'm Dr. Kara. I have over 20 years of experience as a veterinarian and I'd like to help with your concerns about Tammy and her hyperthyroid disease.
An older cat that has a good appetite yet continues to lose weight makes me think of hyperthyroidism (a tumor of the thyroid gland that produces too much hormone).This is easily diagnosed with a blood test, and sometimes an enlarged thyroid gland can even be palpated upon exam. High levels of thyroid hormone cause a higher then normal metabolism which leads to weight loss even with a great appetite, a fast heart rate and hypertension, kidney or liver damage, secondary heart disease, and possible bleeding in the eye or a detached retina so we do want to treat it.
Hyperthyroidism is controllable with medication called methimazole, either orally or a topical gel put on the ear, a prescription diet called y/d which is very low in iodine so too much hormone can't be made or radioactive iodine to kill the tumor cells. Some cats have trouble taking the oral medication. It can cause vomiting and diarrhea. Given what you have told me your veterinarian is recommending the y/d diet or the topical gel, both of which are reasonable alternatives.
I hope that this information helps, please let me know if you have any further questions.