Grendel's mother came to Heorot for revenge and to reclaim her son's dignity. There really is nothing "noble" from any perspective from death by amputation. Grendel did not go down fighting, but he rather ran away, leaving his arm behind. He made his way back to momma, bleeding as he went. The wound was fatal, and Grendel's memorial was in his humiliation at the hand of a mere mortal.
Grendel's mother, then, in her rage, went to Heorot for two things: retaliation and reclamation. Retalitation came when she killed Esher and kept his body. (She later floated his head on the lake for the soldiers to see, thus ensuring retaliation for both the death and the humiliation.) Reclamation came when she took Grendel's arm down from the rafters and carried it home with her.
Grendel’s mother made her way to Heorot to avenge her son’s death after the monster sustained a fatal wound during the fight with Beowulf. Grendel attacked the Thanes in the mead hall until they abandoned the building. The warriors were unable to contain the beast as it wrecked havoc on Heorot each passing night. Beowulf from the Geats heard of the woes befalling the Thanes and took up the challenge to stop Grendel. Beowulf traveled together with his band of warriors to the land of the Thanes. After the introductory festivities, Beowulf and his band of warriors slept in Heorot waiting for Grendel’s arrival. Grendel fought with Beowulf, but the monster proved no match for the great warrior. The monster was forced to flee leaving behind its bloodied arm. The arm was later displayed at Heorot.
Grendel’s mother arrived in Heorot after the ceremony held on behalf of Beowulf, to thank the warrior for his victory over Grendel. The warriors were resting in the mead hall when Grendel’s mother grabbed Aeschere, a warrior most dear to Hrothgar and her son’s bloodied arm that was on display. She quickly made her way back to her lair.
That hag was in haste, wanting to flee with her life when the liegemen spotted her. However, she seized a single clansman firmly as she fled to the moors. He was the dearest of heroes to Hrothgar; a trusty vassal among the oceans was he whom she killed upon his couch—a mighty shield-warrior. Beowulf was not there—another house had been set apart for the renowned Geat after the gift-giving. Heorot was in an uproar, and the hag took the famous blood-spattered hand.