To delete your Grok chat history on grok.com/app and X, go to the chat settings...
https://blogfreely.net/samuel-wang09/whats-the-safest-way-to-keep-a-copy-of-one-important-grok-thread
To delete your Grok chat history on grok.com/app and X, go to the chat settings and select “Delete History.” Remember, deleting chats won’t remove any files or Imagine media—they need to be deleted separately from their folders