How can I take off a passcode from an iPod with a broken screen?

I am needing to transfer apps from an iPod Touch 4th gen that has a broken screen, to an iPod Touch 5th gen. Unfortunately, when I go to back up the 4th gen in iTunes, it won't let me because it needs the passcode, which I can't do because of the broken screen.

Is there a way to delete the passcode through the computer? Through iTunes? Other? I don't really want to spend $100 to fix the screen for the sole purpose of getting the passcode.