Why is an un-deletable Springboard app on my screen after the iOS 6 upgrade?
Before going through a hard reset, it might be worth doing a soft reset.

To do that, press the Power &amp; Home buttons simultaneously until the iPod shuts down by itself. Release the buttons and power it back on.

This might take care of the issue. Otherwise, just restore it using iTunes and if you have no valuable data to lose, choose the "Setup Up As New Phone" option.