If you have deleted a folder from your email account but it is still showing up in Boxer, syncing the folder list should properly remove it from Boxer. To do this:
1. Open up the slide-out navigation pane.
2. Select the email account under 'Accounts' that has the old folder visible.
3. This will open up the list of folders for that account and sync them.Once you return to the inbox and then view the folder list again, the old folder should no longer be visible.
It's also possible that the folders are in the trash folder of your desktop email, and have not been fully deleted from the server. Try emptying the trash folder at your desktop, syncing the folder list, and then check to see if the folders are still there.