When Grendel first experiences Beowulf's strength he exclaims, "Nowhere on middle-earth, I realize, have I encountered a grip like his." (168)
Gardner's use of "middle-earth" is striking because it seems to allude so openly to J. R. R. Tolkein's mythical land from The Lord of the Rings books and The Silmarillion (reviewed by JG in the New York Times, 10.23.77). It may be worth remembering Grendel was published in 1971 during the first wave of mass enthusiasm in America for Tolkein's work.
But we do not need to look so far afield. Gummere's 1910 translation of Beowulf describes Grendel at this same shocking moment:
Seamus Heaney's (2000) translation abandons the term altogether:
The Old English term in question is "middan-geardes", which is sometimes translated as "world" and other times as "middle-world". It is easy to imagine the theological value of this term for seventh century Christians who strove to make a point about the precise location of this impermanent world. It is in the middle, south of Heaven and north of Hell.
But the non-Christian roots here are more convincing. Norse mythology tells of the creation of the earth from the body of the dead giant Ymir:
The online Tolkein reference work Encyclopedia of Arda notes
It is most likely that Gardner is simply translating from Beowulf.
Still, it is also possible that Gardner uses a term so familiar from Tolkein's work as an homage to the scholar, whose 1936 paper, "Beowulf: The Monsters and the Critics" was among the first to take the epic seriously as an artistically coherent work of literature. Seamus Heaney makes this point about Tolkein's essay in the Introduction to his translation of Beowulf.