Want to salvage the artwork from a jewel case? I did a few hundred of these in one sitting and I came up with an easy method.
Open the cover. This is tricky, because jewel cases suck so much, but you've probably figured out a technique by now.
Remove the liner notes. That's the booklet inside the cover.
Flex the case. (This is the magic step.) Right near the hinge, pull the top and bottom edges back and push the middle out. One of the corners of the tray should pop out.
A two-handed technique requires less hand strength and is
probably easier to figure out.
I use a one-handed tiger-style grip, which is faster since
the other hand can start on the next step right away.
Pull out the tray.
If you moisten your thumb, you can pull the tray card out easily.