I read a lot of C&D letters from celebrities here and on Reddit, and a lot of them are in the form of "I am important so I am requesting that you do not take advantage of your legal rights." I am not a fan. (If you don't want someone to track how often you fly your private jet, buy a new one for each trip. That is the legal option that is available to you. But I digress...)
Thinking about that episode, I imagine the legal risk is less in trying to sound like Scarlett Johansson, and more in trying to sound like Samantha, the AI character in Her. Warner Brothers or Spike Jonze probably has some legal rights to the character, and an argument could be made that OpenAI was infringing on that. The viability of that argument probably depends on how much people conflate the two or believe that the one was meant to represent the other.