To delete your Grok chat history, go to grok.com/app or X and remove the chats...

https://lukasnpyy234.cavandoragh.org/how-do-i-delete-grok-chats-on-a-shared-computer-safely

To delete your Grok chat history, go to grok.com/app or X and remove the chats directly. Remember, this won’t delete any files or Imagine media—you need to delete those separately