Greid's place in Culhwch and Olwen begins with the court's network of named companions. Culhwch appeals to Arthur and invokes a remarkable assembly of people whose identities often survive in only a few words. Greid is identified through Eri, his father. A patronymic establishes that relationship, but it does not tell us Eri's occupation, rank or adventures. Nor does the roll-call itself prove that every named figure once possessed a lost epic. Greid's surviving importance comes from the particular connections that the tale preserves, rather than from a reconstructed biography supplied to fill its gaps.

The captivity episode places Greid among those defeated by Gwyn ap Nudd. The conflict begins when Gwyn takes Creiddylad from Gwythyr son of Greidawl, prompting Gwythyr to gather a fighting force. Greid is one of Gwyn's prisoners, alongside men whose misfortunes are described with differing degrees of detail. The episode includes the killing of Nwython and the torment of his son Cyledyr. Arthur hears of the violence, travels north and brings Gwyn before him. He frees the captives and imposes a settlement under which the rivals must continue their contest each first of May until the final judgement.

Greid's imprisonment is also recalled during the search for Mabon son of Modron. The Salmon of Llyn Llyw carries Cei and Gwrhyr towards Gloucester, where they hear a prisoner lamenting. It is Mabon, not the salmon, who compares his confinement with those of Lludd Silver-hand and Greid son of Eri. He says that his own imprisonment is worse. The comparison gives Greid's name a place among remembered sufferers, but it does not put all three men in the same dungeon. The separate passages should not be expanded into a continuous account of their shared captivity.

Drudwyn supplies Greid's other important connection. Ysbaddaden requires the hound for the hunt of Twrch Trwyth, and the tale surrounds its handling with extraordinary demands. The task-list names the leash of Cors Hundred Claws, rendered Cwrs Cant Ewin in Guest's translation, along with other necessary equipment. A later episode also says that a leash for Drudwyn must be made from the beard of Dillus the Bearded. Cei and Bedwyr obtain that beard while Dillus is alive. Both requirements occur in the consulted text; they should be acknowledged rather than silently rewritten into a tidier single equipment list. Greid owns the hound, but the beard-taking is the companions' deed.

The Three Exalted Prisoners in the Welsh triadic tradition provide a useful comparison, but Greid's appearance in Mabon's speech should not automatically make him the fixed third member of every version of a triad. The supplied account also mentions Gwair, and explanations of a substitution belong to scholarship rather than to explicit narration of Greid's life. What remains secure within the tale is compact: Eri is his father, Drudwyn is his hound, Gwyn captures him and Arthur secures his release. Those links carry his name through courtly, otherworldly and hunting episodes without turning a briefly described warrior into the hero of events performed by others.