Despite having defeated both grendel and grendel's mother, Beowulf still seeks final revenge. What does this say about his character?

Beowulf decapitated both Grendel and Grendel's mother even though they are already dead. This shows how thorough Beowulf is. He took Grendel's head and presented it to the people to show that he has killed the monster but all glory goes to God who have help him defeat his enemies.