Sender-anonymous end-to-end encrypted messaging allows sending messages to a recipient without revealing the sender’s identity to the messaging platform. Signal recently introduced a sender anonymity feature that includes an abuse mitigation mechanism meant to allow the platform to block malicious senders on behalf of a recipient. We explore the tension between sender anonymity and abuse mitigation. We start by showing limitations of Signal’s deployed mechanism, observing that it results in relatively weak anonymity properties and showing a new griefing attack that allows a malicious sender to drain a victim’s battery. We therefore design a new protocol, called Orca, that allows recipients to register a privacy-preserving blocklist with the platform. Without learning the sender’s identity, the platform can check that the sender is not on the blocklist and that the sender can be identified by the recipient. We construct Orca using a new type of group signature scheme, for which we give formal security notions. Our prototype implementation showcases Orca’s practicality.