You must mean no resident grizzly tag is required in Unit 20D. Residents don't need black bear tags anywhere in Alaska. For black bears in all of Unit 20 there's no closed season and the bag limit is 3 bears per regulatory year. As a non-resident you'd need a hunting license ($85) and however many black bear tags you care to buy ($225/each).

If you're going to be bummed if you don't find a moose antler prepare yourself to be bummed. I've never found one in all my years of bumbling around through the boonies up here. I've found a ton of caribou sheds though. I've never been around Mt Harper though so maybe the moose sheds areall over there. In general the combination of the very low population densities of moose (compared to other big game animals), their tendency to live in very brushy areas, and all of the gnawing rodents such as squirrels, voles, porcupines, etc. means that the odds of finding moose sheds is pretty slim. People that do it with any regularity general use planes to spot them from above and they know the areas where the bulls tend to yard up in the early winter when they shed.

AK Jeff