To delete your Grok chat history on grok.com/app or X, go to your 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 or X, go to your chat settings and select delete conversation. Remember, this only removes text chats. Files and Imagine media stored in your account must be deleted separately