To delete your Grok chat history, go to grok.com/app and remove messages...

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 and remove messages directly from the conversation. Don’t forget to check the Recently Deleted folder—it holds your deleted chats for 30 days before permanent removal