Talk to the guard at the museum and then click ur cape, or try to wear the cape thats on display... if that doesnt work you may have to purchase another comp cape to wear it.. its a bug
If it shows you have 77/77 for Comp and 69/69 for Comp (T) done, you just need to talk to the Museum guard next to the comp cape stand in the Varrock Museum (or interact with the cape in the museum) and it should resolve itself. If not, a bug report is recommended.