You can permanently delete an archived conversation.
To do this, use the "Trash" filter of your conversation listing, click on the Action selector in the line the conversation that you want, and select "Permanently delete".
You can also permanently delete multiple conversations. To do this, check the conversations that you want to modify then click the Grouped actions selector at the top of your talk page and click "Permanently delete".
Your conversations will be completely deleted and will not be visible at all in your admin area. You cannot restore them.