In general there's a good chance ClO2 will interfere with medication by neutralizing harmful chemicals. In many cases such "interference" would be beneficial. But then, again generally spoken, dropping the medication all together oftentimes is beneficial as well.
Dietary changes and certain supplements like iodine may in fact both kill cancer and help regenerate the thyroid by time. Medication mostly mask symptoms for a while and give side effects, not heal the cause.
If it were my thyroid cancer I would sure drop medication and go for some intensive ClO2 and DMSO treatment. Because that is what I have and do count on. Combine with dietary and lifestyle changes, if she's not already doing that. As a husband, or family member or friend for that matter, I would do the same protocols. For emotional support and help getting into different daily routines, and maybe drop some old habits.
May this help motivate her give it a try.