In January 2026, newly unsealed documents showed that Karp had corresponded by email with Jeffrey Epstein on personal matters. One such correspondence involved Karp asking on behalf of his son, a filmmaker, for an opportunity to work with Woody Allen. He wrote to Epstein in 2015, "I can't thank you enough for including me in an evening I'll never forget... It was truly 'once in a lifetime' in every way, though I hope to be invited again", and praised Epstein in an email, saying "you're amazing." Karp also corresponded with Epstein as part of an attempt to surveil an unspecified woman and have her deported.

Paul, Weiss stated that Karp did not have a professional relationship with Epstein and that neither Karp nor the firm represented Epstein as a client.

He resigned from Paul, Weiss on February 4, 2026, after the correspondence with Epstein became public