Beowulf had hoped to have an entire Grendel body to present to King Hrothgar after his battle with the ogre in Heorot. He has to settle for the right arm or claw, ripped from its shoulder socket, when the mortally wounded adversary flees to the swamp. The claw is hung high beneath Heorot's roof (most likely on the outside beneath the gables) as a symbol of Beowulf's victory.
Grendel's mother also sees it as a symbol, representing her personal loss and mankind's macabre sense of what might be an appropriate trophy. Filled with grief and rage, she retrieves the arm from Heorot and kills another Scylding in the process. When Beowulf tracks her to the mere and ends up in her underwater cave, he has no more interest in the claw. Grendel's head, which he is able to find after a strange, perhaps holy brilliance illuminates the dimly lighted cave, is much more impressive. He ignores the vast treasure in the cave, instead choosing to carry the magnificent, huge head as symbolic of his victory over both ogres.
