Modern software security increasingly relies on bug bounty programs, which incentivize independent researchers to discover and responsibly disclose vulnerabilities. While effective in traditional software ecosystems, these programs face unique challenges in the context of smart contracts. Smart contracts run on blockchains, manage financial assets, and are typically authored by pseudonymous developers. As a result, when vulnerabilities are discovered, security researchers often lack a secure and reliable channel for disclosure. Existing workarounds, such as encrypting messages to contract authors' public keys, introduce inefficiencies and privacy risks, since ciphertexts themselves may reveal the presence of bugs. We propose DeadDrop, the first system to support oblivious bug reporting for smart contracts. DeadDrop combines oblivious message retrieval (OMR) with a trusted execution environment (TEE) to enable researchers to privately and efficiently deliver vulnerability reports without revealing their intended recipient or overwhelming authors with spam. Our design specifies security requirements for such a system, presents practical techniques for handling long messages, and introduces a bug specification language to formalize submissions. We implement a prototype and evaluate its performance, demonstrating that oblivious bug reporting is both feasible and efficient, achieving an amortized processing time of approximately 3 ms per submission. Finally, we discuss incentive mechanisms to encourage participation, highlighting open challenges for decentralized bug bounty ecosystems.