Brief Answer:
Thyroid

Detailed Answer:
If your thyroid ablation was performed for thyroid cancer, then typically quantitative thyroglobulin is measured in the blood along with anti thyroglobulin antibodies, for a specific reason. This is so because the thyroglobulin levels in the blood can be misleading in the presence of positive anti thyroglobulin antibodies. In such a situation, doctors cannot rely on blood thyroglobulin levels as a marker of thyroid cancer.
However, if your ablation was done for an over-active thyroid either due to Graves disease then usually the entire thyroid gland becomes under-active and the above-mentioned antibodies are not generally required.
If the ablation was done for a single over -active nodule, then typically the remainder of the thyroid often functions normally afterwards. In such a scenario, it is conceivable that your doctor might want to run the above antibody tests to get a fair idea if the rest of the thyroid gland is likely to be affected by this 'auto-immune' disease called Hashimoto's thyroiditis. Positive antibody results as is the case with you tend to indicate that you may well be at a higher risk for future development of this condition, which often leads to a permanently irreversible thyroid state. Ultimately this necessitates lifelong treatment with an oral medication called levo thyroxine.
And finally, the third common reason for undergoing a radio active iodine ablation is 'Toxic Multi Nodular Goiter" in which there are several over-active thyroid nodules. After ablating these, many a time the thyroid is rendered irreversibly under-active for life. But is the thyroid function after ablation is normal, then the antibody test results may give an idea as to the chances of the thyroid becoming under-active in future.

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Brief Answer:
Follow up

Detailed Answer:
Thyroid antibodies are also referred to thyroid auto-antibodies. They are so called because the antibodies attack one's own normal cells, hence the term auto. This is obviously abnormal because the usual function of antibodies is to protect us from infection. Instead these antibodies damage our own cells and organs leading to poor function. In this instance, these thyroid auto-antibodies destroy the thyroid gland, often rendering it inactive for life.The name of this medical problem is Hypothyroidism due to chronic Hashimoto's thyroiditis. This irreversible process mandates treatment with thyroid medication called levo thyroxine to replace the missing hormone which the damaged thyroid can no longer make.
Graves is an example of an auto-immune thyroid disease. It is however the opposite of hypothyroidism, and leads to hyperthyroidism ie an over active thyroid. The auto-antibodies in this condition are usually of a different kind. They are called TSI (Thyroid Stimulating Immunoglobulins) or TRABS (Thyroid Receptor stimulating Antibodies). But your doctor has ordered the other variety of antibodies as described above. You can ask him for his reasons to do so.
Ablating the thyroid with radio-active iodine generally has no impact on the presence of antibody levels in the blood.

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Brief Answer:
Second follow up

Detailed Answer:
Presence of thyroglobulin and thyroid peroxidase antibodies does not mean the thyroid is absent. It indicates the presence of antibodies that tend to attack the thyroid cells and make it under-active.

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