The battery case is snug because of the seal that keeps RunScribe water resistant.
There are lock and unlock icons on the back of the RunScribe. A dot is printed on the battery door. When inserting the battery, align the dot with the unlock icon, and then rotate it to the lock position.
If you can't open the battery door with your fingers, use one of the clips for leverage, nudge it against the cutouts in the battery door, and rotate the battery door into the lock or unlock position.