This is a difficult one. Scientifically, I wouldn't have thought the difference would be enough to be concerned about considering the rather large deficit of calories in this diet.
Having said that, I have an underactive thyroid (okay...thyroid is actually alright, but I have a syndrome that attacks the natural thyroxine) and I probably lost a little less than most others.
It still averaged out about 12lbs a month though, which is way more than other diets.
If it's you with the underactive thyroid, are you taking anything for it? I They can't seem to get my levels up however much thyroxine I take, but most people take adequate amounts of artifically thyroxine to bring them back to normal levels. It then shouldn't make any difference, whatever their previous diagnosis