Island Geirsholmur is a small and round shaped island near the headland tyrilsnes in the Whale Bay.  It is mentioned in the Sturlunga Saga and the Hardar Saga.  The principal hero of this saga, Hordur Grimkelsson was the chief of a band of robbers, who lived on the island until they were tricked and killed.  Hordur magaged to kill 13 men before he was slain.

His spouce, Helga Jarlsdottir, did not believe in the promises of their pursuers, and stayed behind on the island.  Later, she managed to swim with her two sons, four and eight years old, ashore.  The younger son held on to the mother, and the older one she helped the rest of the way after having left the other one on the shore.  The three of them then climbed Mt. Tyrill and continued to valley Skorradalur, where they found shelter.  During the early part of the Sturlunga Period, Sturla Sighvatsson and his men occupied the island for a while.