I'm not a doc either, but...
With or without a thyroid, the body has a metabolic rate and requires a certain amount of energy to perform its daily tasks. Without a thyroid the metabolic rate will be significantly lower (i.e. body will use fewer cals in a day, which is why hypothyroid folks gain weight or have trouble losing it).
But the underlying physical laws remain: if the body is burning more calories than it is taking in, weight loss must occur (the body cannot create matter from nothing).
The issue is that calorie reduction and activity increase will have to be greater than normal to see the same results. So the approach is identical--just magnified to compensate for the lower MR.
Take Connie's advice and have her keep a very detailed log of food and training. Do the math on the calorie intake and then start dropping it incrementally and see what happens. The basic idea is to reduce calories as much as possible without compromising energy/performance too greatly.