It looks to me like the Stock Positoning Systems unit, which to me looks like a Graco "Adjustable Butt Plate" (not to be confused with an "Adjustable Pad Plate" used on the "Gracoil System"), but I know nada about either, except that I considered getting one.
http://stockpositioning.com/products.htm I don't see any istructions on either company site, but as designed I see why you would have to remve the top screw. Like Jim said, call whoever's product it is who you got it from. I don't think it is defective, unless the screws don't torque. I bet they will suggest blue loc-tite if you have to remove the upper screw. Let us know what happens as I am interested in the same unit.