Should I put grease on the surfaces of a back pedal internal brake? When servicing a back pedal brake hub, should I put some grease on the internal brake surfaces or not?

Is grease good because it makes the brake run smooth, or bad because it makes it slip and not work so good?
There is no part inside a coaster brake that can be harmed by grease.  You do need to use a high-temperature grease though, friction makes them get quite hot.