Normally when my hermit moults I don't get the chance to go near the moult skin. It gets pulled back into the shell and eaten!
As far as I know most critters will eat most of their moultskins given the chance, as it allows them to recover nutrients. So I'd say just leave them for a couple of days at least then pull out anything left, but without disturbing the animal in any way, as stress during a moult or before the new skin hardens can be fatal.
Hope this helps,
Wilf