Apple (AAPL) on Friday made good on the promise Steve Jobs made — with some ill humor — a week earlier. It issued refunds to customers who had purchased its $29 Bumper and it launched a free app that gives iPhone 4 owners who have a problem with its external antenna a choice eight different cases.

If you bought a Bumper, you should have received an e-mail overnight alerting you that your account was being credited.

If you bought an iPhone but not an Apple-brand Bumper, you can download the iPhone 4 Case Program app here.

If you bought a third-party case, you are out of luck.

It has been suggested that the peevishness with which Jobs delivered the message last week  — “Why don’t you give everybody a case? Okay, we’ll give you a free case” — might have something to do with the revenue he was forgoing. Estimates put the profit Apple might have made from the sale of cases in the current quarter at $100 million (5 million Bumpers times $20 profit each).

In any event, iPhone 4 owners who have been experiencing antenna attenuation issues will have to live with them a bit longer. None of the free cases Apple offers ships in less than 3 to 5 weeks.

See also:

• How Steve Jobs turned a finger spot into a death grip
• Did Apple solve its PR problem?
• iPhone 4: The Consumer Reports fiasco
• How bad is the iPhone 4’s signal loss?
• The iPhone 4 Death Grip saga

[Follow Philip Elmer-DeWitt on Twitter @philiped]