Speaking from your actual ethnic side of the pond here, most doner/gyro meat is held together by fat not filler.

It's ground lamb mixed with spices and extra fat. I know because Mom's bf is a Turkish Cypriot who owns a restaurant! Very handy that.

Eat the meat and salad, stay way from the pita and you'll be fine. Or just get souvlakia (the cubed meat) instead.

You can make your own using the sliced meat method as well. That way you can be sure that it's all meat.