How do I get this shower head holder off the wall?
These can definitely be challenging. Some manufacturers use a Philips screw, while others use an Allen screw. At least, these are the 2 most common types. Either way, remember they're used in an area that is damp and some corrosion may build up in the slots or hole, so you may need to use a little more upward or downward force, opposed to turning force, into the set screw than usual when turning.
So, if you only tried using a Philips screwdriver, try using a variety of metric and standard Allen wrenches.
Good luck!