Final answer:
Beowulf cuts off Grendel's head before he leaves the lair as a trophy of his victory, which is the correct answer to the student's question.
Step-by-step explanation:
The last action that Beowulf takes before he leaves Grendel's lair in the epic poem is not specifically described in the provided reference text. However, in the full narrative of the Beowulf epic, the hero does perform a significant action after defeating Grendel's mother that aligns with one of the provided options. After slaying Grendel's mother in her underwater lair, Beowulf locates Grendel's body and decapitates it, taking Grendel's head as a trophy. Therefore, the correct answer to what Beowulf does before he leaves the lair is c) Cuts off Grendel's head.