That tool is used to stop the clutch plate from rotating while you unscrew the shaft nut. It doesn't remove the pulley. It is handy to have though, otherwise you need to improvise for example a screwdriver against the rivets on the plate.

 

Lol, the ebay seller just sent me pics on getting it off. Yeah, guess I spent $15 without needing to



I'll just dismount the compressor and use the pullers the shop has......or use a couple small pry bars.