Core charge? From a wrecker? That was implemented to ensure that the reman place had the "core" to work with when doing a reman... for stuff that doesn't get remanufactured, if it isn't, it should be fraudulent to charge a core charge.
You'd be amazed at what they charge core on, they charged me a core on every Up-Country spring I pulled off that '96 ZJ a few weeks back. I couldn't believe it.