Apple has already begun to automatically refund customers who purchased an iPhone 4 Bumper case using a credit card. You can check on the status of your credit card refund on the Apple iPhone 4 Bumper Refund Program website.
Here are instructions for everyone else who needs a refund.
If you purchased a Bumper using cash, check or gift card at the Apple Store:
Those who have purchased their iPhone 4 before July 23, 2010 must apply no later that August 22. Everyone else must apply within 30 days of purchase. To get a free case, your iPhone 4 must be purchased by September 30.
After a little more than a week of waiting, Apple posted details today about how early iPhone owners can go about landing their $100 Apple Store credit.
Straight from the horse's mouth, here is who qualifies:
If you bought your iPhone before August 22, you may be eligible for an instant $100 electronic credit toward the purchase of products at the Apple Retail Store or the Apple Online Store.
(If you purchased after August 22nd, you can recover the entire $200 difference through Apple's price protection plan.)