Amazon has announced that they will and have been refunding app purchases made by children.
Amazon have been in a three-year long legal case with the Federal Trade Commission in which the FTC accused Amazon of charging customers for unauthorized purchases made by children.
In 2014 FTC approached Amazon on several occasions urging them to introduce tighter security measures when making a payment, such as a password protection or a set of security questions. Amazon denied the request stating that their security precautions were enough and were adequate. Amazon initially offered customers gift cards as a way of reimbursement, but they have now agreed that they shouldn't be charging customers for these unauthorised purchased and are issuing full refunds.
Amazon has had to pay out refunds amounting to $70 million in total due to children buying things that they shouldn't. So if you were charged for a purchase made by your child from November 2011 to May 2016, you will be likely to be able to get your money back.