I'm not sure why the grinding would take place only when shifting into reverse. In theory nothing should be spinning because the clutch is completely disengaged at idle. No spinning/no grinding.
To test the no spinning/no grinding theory, try shifting with the engine turned off.
Is it possible that either your idle speeds are too high, which would begin to engage the primary clutch, or the clutch itself has a problem? Perhaps the primary clutch is dirty so the parts don't move freely and allow complete disengagement or a bad needle bearing or the Teflon coating is gone from the bushing.