Look inside the mouse and find the locking tab, one of two, near the back of the left/right mouse button cover plate. It's a hook that you'll need to pry apart, see location at left arrow. It may help to use a spudger to lift up on the back of the cover plate at the same time.

There is another locking tab to release but it's obscured. You'll need to use a spudger to pry up on the now widened crack at the back of the cover plate to free up the second tab, hidden from both view and access, but at the right arrow.

Once both locking tabs are free at the back, lift up on the cover plate to disengage the cover completely.