Do banks normally keep a backup key to your safe deposit box?

If (big IF) the bank is practicing any kind of security, that $125 will go toward swapping the lock out for another anyway, or at least re-keying the existing one.

Yes, that would be a best practice that most likely would be followed. Because if they can open the box with the one key that was given back they can easily replace the lock without having to drill. Then not have to worry about the 2nd key showing up.