Submit a request
Now that you've got access to your purchase history, you just need to submit a request for the unauthorized purchases. Apple's set up a form for this process that helps generate a support request.
Upon visiting that link, you'll want to click the button for Email, which will take you to a form where you enter your contact information as well as the specific details. Find the order number for the unauthorized purchase and enter it in the relevant field. (If you have multiple unauthorized in-app purchases, you might need to complete more than one of these requests.)
In the detail section, enter "Refund for In-App Purchases made by a minor," then submit the request. Apple should let you know — hopefully pretty quickly — the status of your refund.
Preventing future unauthorized purchases
Despite the ease of submitting these requests, you'd probably prefer avoiding having to do this again — and Apple would likely rather not have to refund a whole bunch of purchases again. That's why the company's rolled out a couple of options to make it harder for kids (or us unwitting adults) to accidentally make in-app purchases, all with only a couple steps.
If you're regularly handing over your device to a kid, you'll want to enable parental restrictions, and either turn off In-App Purchases altogether or scroll down to Require Password and select 'Immediately.' That eliminates the occasionally troublesome 15-minute window where, after you make one purchase, subsequent purchases can be made without re-entering your password. It might be more annoying for you, but it could also save you some hassle down the line.
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