Customers who had already bought iPhone Bumpers before Apple offered free cases to all iPhone 4 users have started to receive refunds from the company.

Apple said at last week’s iPhone 4 press conference that it would provide free cases to anyone who buys the iPhone 4 before September 30. That free case offer includes a choice of either Apple’s Bumper or a third-party case. Apple said it would offer refunds to iPhone 4 users who had already bought Bumpers from Apple as part of that offer.

Some customers who bought their Bumpers from Apple’s online store on Thursday reported receiving refund notices from Apple. The message from Apple begins by informing the customer of the situation, and that “as of today, we have automatically processed your refund.” Apple is also refunding shipping and VAT charges as well.

So far, there is no word on how many customers have gotten refunds or how long this automatic refund process for online Bumper orders will take. Apple also has yet to announce how customers who purchased Bumpers in retail stores can go about getting a refund.

(Thanks to Macworld and aido2002)