To delete your Grok chat history on grok.com/app and X, go to your chat...

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 your chat settings and choose “Delete History.” Remember, this clears only chat messages—files and Imagine media must be deleted separately