



The whole business makes little sense, because it’s ultimately easier and faster to simply remove the thing. No damage to the wall, and then wallpaper can go behind the fixture leaving no cut edges around it.



In the top photo, I am using an allen wrench to remove the tiny set screw that is holding a toilet paper holder to its mounting bracket. Turning the screw causes the wrench to rub against the wall, and the metal is leaving a dark mark on the wallpaper primer. You wouldn’t want this to happen once the new wallpaper is up!
To prevent this, you could put a piece of scrap paper in between the wrench and the new paper. Or you can make tiny, 1/4 turns, so that the large end of the wrench does not come in contact with the wall.
Or, better, use a smaller wrench with a narrower profile. These are usually included in the box when you buy fixtures like this. As you can see in the second photo, there is plenty of clearance, and no damage to the new wallpaper.
Many bathroom fixtures (towel bars, etc.) are removed by the use of an allen wrench (also called a hex key). My American (inch) set on the left works most of the time.
But it helps to have a metric set (right) on hand, too, for the occasional fixture calibrated to European measurements.