I had a Wells Fargo Visa Debit card that I could not load after I restored my iPhone 7 plus from a backup. I called Apple and they said it was Wells Fargo. Wells Fargo said it was Apple. I called Apple back and they then said to contact Visa. You can't contact Visa about Apple Pay issues!
So I then set about trying one thing after another. I got a new Visa debit card with the same card number but with a different expiration date and security code. It didn't work. I then got a new Visa debit card with a new card number. It didn't work. I upgraded to 10.3.1. It didn't work. I restored from my backup again after upgrading to 10.3.1. It didn't work. I hit upon trying to the idea of trying to "Set Up as New iPhone" while searching the internet. In the Apple Support page that guides you through this process it mentions selecting this option in the "Apps and Data" screen. However to get to that screen you have to go to "Settings > General > Reset > Erase All Content and Settings" in your iPhone. After doing this, I was able to, at last, reload my Wells Fargo Visa Debit card. I then unloaded it thinking that this would reset the "Wallet" to accept the card again after I reloaded from my backup again. It didn't work. So I tried to do the same thing again but this time leave the card loaded in the "Wallet" and reload my backup. It didn't work.
Finally, I thought about why I could reload my card after I reset my iPhone by erasing all content and settings. It dawned on me that the "Wallet" settings are somehow corrupted when you restore from a backup. So I decided to try and "Reset All Settings" instead of "Erase All Content and Settings." Low and behold it worked! Granted, I had to go back through and reenter my settings but all of my "Content" was exactly as I had had it previously. This included the screen layout, Contacts, Calendar, Reminders, Notes, Music, Messages, Mail, everything that was really important and I now can once again use Apple Pay!
It would be nice if Apple would add a "Reset Wallet" option so that you wouldn't loose your other settings but I'll take the later rather than replacing my iPhone or switching banks!