The various Mamiya grips are all compatible in fitting onto the screw thread and two locating pins on the camera base. However, the grips designed for the C330 and later cameras include a trigger button that links to the front shutter release of the C330. On the C220, there is no such shutter release, so the actuator does not fire the shutter.
I had a pistol grip for my TLRs (I have owned a C3, C220, and still have a C330f). My favorite grip was not a Mamiya brand, wish I could remember the brand, but it had a replaceable cable release at the trigger that was long enough to also go to the top screw of the C220. You should have a threaded cable release there, which is not on my C330. I also looked at ebay and there are several there that should work.