The traps just hold the animal. If used correctly, they do not even hurt the animal in any way.
I don't fully agree with that. It will break the skin of the animal, and depending on the size of the trap and temprament of the animal they can inflict a lot of damage to their feet. I've heard of instances where they chew their leg off to get out, but have not experienced it. Most of the animals I caught had some damage to their legs, but would heal with time.