The clamp consists of 2 parts, an inner part that is usually screwed into the wall and the next chrome cover cap that is clamped on and snaps into place.
Sometimes you press a little inward into the hole and pull a bit outward on the chrome piece to separate it.
I only found a picture of one with 2 tubes in it, but it's often the same or a similar principle
snap fasteners that you either poke into holes or bend a little outward so the plastic comes loose.