Bonus point systems are widely used for rewarding customer loyalty in both traditional and electronic commerce scenarios. Merchants aim to additionally increase revenue by targeted advertising using customer data. At the same time, customers wish to protect their privacy of what they purchase. Common systems neither provide sufficient protection of privacy, nor protect the customers' identities. Anonymity makes it significantly harder to properly resolve claims of fraudulent transactions, because identities are not recorded for any purpose after a transaction has been committed. We propose an anonymous bonus system based on digital payment systems using blind cryptographic signatures. We implement a protocol extension that allows proof of bonus point possession in case of reported misbehavior, and we identify the implications on security, privacy, and performance of our proposals. Our results show that we can resolve these cases of fraud within the system without losing functionality in the bonus point protocol.