The grips come polished with a white polishing rough which has some waxes and oils in it.
Stag grips will require little care down the road but adding a little extra shine with a good clear furniture polish or automotive wax will do the trick.
When light cleaning your gun removing the grips is not generally necessary but a full tear down and cleaning should be. Remove the grips from the frame to ensure they do not get over saturated with cleaning solvents.