You'll hear a noise that will sound horrible.......BUT...
...everything will be fine.
Here's what I do: Reach as far under the cover with one of your fingers, and just pull - slowly - away from the reader. The covers are joined at about 4 (?) places on the Reader. As each one comes off, you'll hear this horrible sound. But everything will be fine.
The first one to come off is probably the one that is the "hardest," in that once you "remove" it from the Reader, there are only about 3 (?) left. Keep in mind these "grippers" really do work.
You should do this while sitting on the couch, so that if you drop the Reader, then there's not a far place for anythng to fall.
It's really easy....but I also remember my horror upon hearing that sound as the plastic hinge lets go of the Reader.
I hope this helps.