How can one be absolved from a transaction involving the exchange of old gold for new, with a difference paid, which turned out to be usury (riba)? Is it permissible to sell the new gold to the same merchant, keep the price of the old gold, and give the difference in charity?

Jewelry is a matter of differing opinions among scholars. The majority of them hold it to be forbidden, while Ibn Taymiyyah and Ibn al-Qayyim permit it. According to their view, nothing is incumbent upon you. According to the view of the majority, the transaction is rectified by returning the new gold and taking the old gold, along with the cash difference, because the sale is فسخ (annulled). If it is not possible to return the sale, then there is no blame.