If you are going to keep it, put it in a 2X2 to keep it from falling off the coin. They can never be put back if they fall off. I probably wouldn't save it. I'd wait for a real nice one to keep both pieces of.

This one brought the find thousands of dollars, but it was all up to the buyer to get it at auction. Like I aways say, the bigger the error the more interest in them. (Yes he removed the lamination very carefully. So there are cases where you remove them. But almost 99% of the time it is best left intact.