Can I undo the upgrade to iOS 7 by restoring to iOS 6.1.3?
It is likely the baseband was updated along with the OS, but if you have a good backup of the phone, I might try restoring it in recovery mode.


Power off the iPhone
Plug in the iPhone to your computer via USB.
Press and hold the "power" button with one hand for 3 seconds
Hold down the "home" button as well for ten more seconds
Release "power" button but continue to hold "home" button until device enters recovery mode.


I don't have a device to test this and it might not work. You might have to get a jailbreak tool to modify the OS and/or firmware of the device and then restore 6.1.3 on it.