No, but your customer is in their legal right to claim back the VAT. Unfortunately, the Tax Administration does not facilitate a VAT refund to private persons (they do to companies). VAT refunds for travelers can only happen via the merchant.
Check Customs' website
The VAT refund regulation lets you refund the VAT to your international customer instead of transferring it to the Tax Administration.
We often hear merchants complaining about the administrative hassle when dealing with VAT refund. When cooperating with us, we will unburden you and take care of most of the hassle. You need only to offset the VAT, which is similar to handling a suppliers' invoice. Providing a VAT refund is more about helping your international customers claim back the VAT. As a consumer, you might want others to grant you this chance when you shop in countries outside the EU and become eligible for taxfree shopping.