The character with human molars for cuff-links is Meyer Wolfsheim, one of Gatsby's underworld connections.
One of Wolfsheim's notable characteristics is his wearing of cuff-links made of human molars.
The strange taste represented by this choice of accessory suggests the oddity of Wolfsheim's character as well as Gatsby's choice of friends.
When Gatsby is killed and Nick attempts to get people to attend his funeral, Wolfsheim declines the invitation, refusing to come.
He is so selfish and insecure that he refuses to attend Gatsby's funeral.
Proved to be a combination of fair-weather friend and criminal opportunist, Wolfsheim's character can be seen as a contrast to Gatsby's, which includes a rather remarkable degree of nobility and idealism when considered in light of his sometimes sinister dealings and lack of affiliation with a moral code.
Meyer Wolfschiem [sic] is representative of Arnold Rothstein, the man who fixed the 1919 World Series in reality. His wearing of human molars for cufflinks is indicative of his crudeness and brutality, as the molars have been probably extracted from the mouth of one of his enemies. Wolfschiem is obviously a low-class man of no breeding such as the East Egg residents (Tom Buchanan excepted).
His association with Jay Gatsby is obviously one involving illegal activities. Thus, his is probably only a business relationship--one of his business "goneggtions"--although he pretends to be fond of Gatsby. Clearly from his dress and his unsavory accent, Wolfschiem is not one to associate with East or West Eggers. After Gatsby dies, Wolfschiem has no more use for the idealistic man who lives in an area foreign to him, nor would he want to make his presence known there where the FBI could connect him to Gatsby, and possibly arrest him.