Lift off the case back.

Underneath, you'll see a sheet of plastic film. It should be possible to remove the battery without removing the film, if you're careful, but I didn't want to risk bending or tearing the plastic.

If you do take the plastic off, beware of maneuvering it over the three springs in the upper left, and the small prong that sticks out over the battery. You'll need to be sure to arrange the plastic carefully over these obstructions when re-assembling.