There is no need to worry.
Radioiodine is now recognized as the safest and most convenient and effective treatment for hyperthyroidism.
The treatment is safe because radioiodine can deliver sufficient radiation to the thyroid gland to slow its function while delivering only a small amount to the rest of the body (the thyroid is the only part of the body that collects and retains iodine).
The radiation exposure to the rest of the body is quite small, because radioiodine remains within the thyroid gland for a moderate period of time, while that not collected by the thyroid gland leaves the body rapidly in urine.

Is your boyfriend still having thyroid problems?

Just wanted to forward the message that i got from my doctor when i did radioiodine treatment (im a man). The doctor said that it is potentially more dangerous for women to do it due to the fact that they have a static number of eggs contra men who constantly produce new sperm. While the radiation exposure to the rest of the body is minimalistic (and hardly even counted for), this means that any exposure to a mans reproductive organ would be solved automatically via the production of new sperm.