Maybe they wont get the full benefit of the hormones that they would have. An excerpt:-
By taking T3 with meals, a patient reduces the amount of T3 that will enter her blood. Some food constituents, such as calcium, bind thyroid hormone in the GI tract. This effectively limits the amount of T3 that absorbs into the blood, the rise of the blood T3 level, and the brief exposure of the heart to higher concentrations of T3. But there is a problem with this approach.
The patient who takes T3 (or T4) with meals won’t have anywhere near an accurate idea of how much T3 enters her blood. Different meals will contain different amounts of T3-binding substances that will reduce the amount of T3 that enters the blood. One meal may contain a small amount of T3-binding substances; another may contain a large amount. As a result, the amount of T3 that enters the blood after meals is likely to vary a lot. Accordingly, the degree to which T3 drives the patient’s metabolism any day is also likely to vary widely.
Taking T3 with meals, then, blurs the relationship a patient and her doctor may look for between her dose of T3 and her metabolic status. The proper solution is simply to reduce the amount of T3 the patient takes on an empty stomach. With this approach, the relationship between a particular dose of T3 and metabolic status will be far clearer.