The suggestion about Henry Palmetto's death is that Gatsby is in with people who make money illegally. Palmetto committed suicide indicating that he was either remorseful or very fearful and that whatever he had done would result in dire consequences for him. There have been suggestions so far in the story that Gatsby made his fortune through some illegal means, possibly bootlegging, and this furthers that suggestion. Later in the chapter, we meet Meyer Wolfshiem, one of Gatsby's very close associates. We quickly discover that he is a gambler and that he was the money man behind the fixing of the World Series in 1919. If people are identified by those they associate with, then Gatsby certainly should be identified as one who deals with the underworld.