In the Cove admin, you have two choices for handling comments you no longer want to show on your site.
Hiding comments will preserve a comment's place in the chat but will hide the comment body and member details.
Hidden comments are greyed out in the Cove admin. You can always unhide or show the comment in the future using the "Show again" option.
You can also fully delete a comment. This removes the comment totally from your site and is irreversible.