Motor mount question

[Pete_89T2]

See attached picture -- On the right side is one of the brand new stock Mazda mounts I purchased; on the left is my original mount. I replaced these as a pair because one of my original mounts had its rubber sheared off.

Note that the new mount doesn't have the metal cup over the rubber; are you supposed to remove & reuse the metal cups from the original mounts?

If so, I may have a problem, being I already chucked one of them (the old sheared off one) and the one I do still have is on there REALLY GOOD and won't budge off the rubber.