Large language models (LLMs) increasingly power autonomous coding agents such as Codex and Claude Code, yet their training corpora may contain confidential credentials exposed in public repositories or collected from private development artifacts, creating risks of memorization and subsequent leakage. Existing extraction audits, however, largely assume access to model weights or token probabilities. In this work, we present a black-box secret extraction framework for commercial, API-based LLMs under output-only access. It comprises (i) \emph{Cross-Validated Secret Knowledge Distillation}, which uses semantics-preserving prompt variants, response cross-validation, and provider-specific format filtering to distill secret-relevant behavior into a local white-box proxy; and (ii) \emph{Proxy-Guided Secret Extraction and Candidate Filtering}, which combines truncated top-$p$ sampling with local token entropy, $N$-gram frequency profiling, and provider-specific structural priors. On controlled API-key benchmarks, our framework improves recovery effectiveness and real-key rates over representative baselines while reducing extraction latency. A responsible real-world evaluation further recovers masked provider-specific credentials from three independently deployed black-box LLM systems spanning OpenAI and Claude Code, showing that memorized secrets can be exposed under output-only access.