The tweeter is just stuck because its been in the same spot for years. Get a couple of really small allen/hex wrenches. Put the short ends of the allen wrenches in 2 screw holes opposite each other. Straighten the allen keys out so they are pointing towards you and the small ends are behind the face of the tweeter. Pull gently on both wrenches at the same time and it should pop right out.
If for some reason that doesn't work, crazy glue something to the face of the tweeter that you can use as a handle, and pull it out that way.
If for some reason that doesn't work, crazy glue something to the face of the tweeter that you can use as a handle, and pull it out that way.