What does Gatsby's friendship with Wolfsheim imply about his own background?

Gatsby appears “shady” by connection. Wolfsheim is clearly doing some dirty business. He’s definitely a gambler, but the creepy human molar cufflinks and business “gonnegtion” (connection) that he starts to speak about is quickly hushed up by Gatsby. This makes Wolfsheim look bad. What kind of person would be friends with this person? What kind of person would actually do BUSINESS with this person? That’s how it looks on Gatsby.