Yes, you can open this case. There are two small hidden screws. They are near the hinge, and under the rubber liner on the inside of the case. You call peel it back with a small, flat tool and maybe some gentle heat to soften the adhesive. Start in the corner near the hinge, where the ear piece sits when the headset is stored in the case.
After removing those two screws, you can pry around the top edge of the case to release the snaps and it should come out. There are some small magnets to retain the headset, so don’t lose them when opening.