In Chapter 9, after the accident and after Gatsby's death the story of each hit the news. Nick suggestst that the affair between Myrtle and Tom was very close to coming out.
When Michealis's testimony at the inquest brought to light Wilson's suspicions of his wife I thought the whole tale would shortly be served up in a racy pasquinade - but Catherine, who might have said anything, didn't say a word.
Myrtle's sister Catherine protected her sister's reputation by keeping quiet "and swore that her sister had never seen Gatsby, that her sister was completely happy with her husband, that her sister had been into no mischief whatever."
It is largely due to this loyalty on the part of Catherine that the affair remained secret.
The only other people who knew about the affair were Tom, Daisy, Jordan and Nick. In the end, Nick's exclusive interest was in Gatsby and he apparently had nothing to gain by spreading news of the affair between Myrtle and Tom. Jordan, Daisy and Tom all distanced themselves very quickly from the accident.