The moves comes after a string of cases where children have been able to run up large bills of in-app purchases when playing games downloaded from Apple's App Store. Viewers had contacted ITV Meridian complaining of the charges incurred - often by children unaware of the costs they were clocking-up while using the App Store.
One incident of in-app overspending resulted in a lawsuit from parents, while a UK police officer reported his son for fraud after he spent more than £3,000 playing games such as Plants vs Zombies using his father's log-in details.
In the past, Apple has introduced an "in-app purchase" label to items on the App Store that do contain buyable extras, as well as an information page on iTunes about how to improve password security on devices to prevent unexpected expense.
The issue stems from a setting within Apple's iOS operating system that can allow password entries to stay active for 15 minutes after they have been entered. This means purchases can be made in that time without having to re-enter a password.
While refunds have been offered in individual cases in the past, this is the first time the company, based in Cupertino, California, has asked customers to come forward and make requests for reimbursement.
The email concludes by offering steps on how to submit a refund request, with all submissions needed before April 15 next year