Thyroid tissue can regrow. One comment on this board was a woman who had a fully regenerated thyroid gland after 40 years!
"Thyroglobulin levels should be undetectable or very low after the surgical removal of the thyroid (thyroidectomy) and/or after subsequent radioactive iodine treatments. If levels are still detectable, there may be normal or cancerous thyroid tissue remaining in the person's body, indicating the need for additional treatment." LabTest Online - Thyroglobulin