The military governor of Hawaii recalled all paper currency in the territory in January 1942, fearing that if the Japanese landed, they could smuggle the millions in circulation to Japanese agents on the mainland. The indelible stamp was meant to make Hawaiian money valueless if an invasion occurred. From July 1942, all paper currency in Hawaii had to bear the "HAWAII" overprint until October 1944, when there was absolutely no further risk of Japanese invasion.
Source: page 99 of the 1945 Report of the Secretary of the Treasury.