You have to leave the conversation. That is how Xenforo deletes them.
Yes, I know. I only just looked myself.
When you click Message icon and then click show all...
do you get a choice to select them by clicking a little box to right of Participants?
You should. If you click box, a red taskbar will show at bottom of page.
If you choose multiple squares, all the ones selected will be added to the count on taskbar.
Then you can pick "Leave conversations" from the menu and it will delete them all once you press Go
If you decide not to clear them all, one choice of the red taskbar is deselect all.
note: Star conversations are ones you have marked with a star in the actual conversation, its used to filter posts you want to find (more useful if you have 28 pages of them). Star button is on top line of all conversations.