How is the story "The Great Gatsby" an ironic inversion of a knightly quest for the grail?
The "knightly quest for the grail" is the search by heroes for that most elusive of objects, the cup Jesus used at the last supper. It is also used to mean anytime an individual attempts to acquire the ultimate object of their desire. In that sense, the grail could be a work of art, a rare fossil, or (as in The Great Gatsby) a human being.
In the Great Gatsby, Gatsby is on a quest to obtain Daisy. All of his actions seem geared toward getting her. He gets rich, moves near her, and throws elaborate parties in an attempt to lure her to him. He engages in subterfuge with Nick and has clandestine meetings with Daisy. In the same way that the nights spend their days trying to locate and acquire the grail, Gatsby does the same thing with Daisy.
The trick is in how your question is phrased: "ironic inversion." Inversion means "to turn something upside-down," which implies that we are looking for how the opposite of the grail story applies to The Great Gatsby. In grail terms, it would be like the grail searching for the knights. In Gatsby terms, it would be like Daisy coming to Gatsby, and that just doesn't happen in the story. Instead of an inversion of the grail stories, Gatsby seems to follow the pattern (including the theme of ultimately being denied.)