For merchants subscribing to Returnly Premium and utilizing any version of Shopify, Returnly offers a separate return flow for individuals who received item(s) as gifts -- giftees. The original purchaser is not involved or notified, so no hurt feelings and the sentiment is still felt!
Gift Return Flow
For a giftee going through the flow, they will see the following "Returning a Gift?" option at your Return Center:

Once a giftee has entered the flow, they will need to enter their Order Number, Zip Code, Name (First and Last), and Email Address within the corresponding fields:
Once their return has been initiated, the giftee will be provided with a shipping label to send their item(s) back.
Post-delivery and upon the returned being processed, and correspondingly transitioned to a status of “Refunded," the giftee will be provided with a gift card (store credit) equal to the RMA's "Refunded" amount.
If you wish to turn on or have additional questions around implementing Gift Returns, please reach out to us at support@returnly.com.