If you paid with a CC, your CC will simply be refunded. No calling, no applying necessary. Automatic.
I highly doubt it because that opens up a can of worms... there's no way to tell the difference between me; ordered 2 bumpers for both my wife and myself and someone who ordered 2 because they couldn't decide which color they wanted.
Also, if they're going by credit card charges, there's no way to tell if someone's Bumper was already refunded when they request the free case. Using a different credit card for instance... or my wife who has her bumper but her name's not attached to it.
It WILL likely be a request service where you register the phone itself by serial number, and get the case or refund based on that.