Answer
Open the Trash tab and choose Empty Trash at the bottom of the list. HelperHat asks once, telling you how many conversations will be deleted, and then deletes every conversation in Trash forever, including ones further down the list that haven't loaded yet. This can't be undone.
The button shows only when Trash has conversations, and it's hidden while you're selecting conversations. To delete just a few, select them and choose Delete Forever instead.
A conversation someone restores while Trash is being emptied is left alone. If some conversations can't be deleted, a message says how many were, and you can choose Empty Trash again to finish.