Large language models are pretrained on massive, largely undisclosed corpora that may contain copyrighted, privacy-sensitive, or otherwise unauthorized content, making pre-training data detection essential for data-rights auditing, privacy protection, and benchmark contamination analysis. However, most existing methods follow a gray-box setting, relying on internal signals such as token probabilities, logits, or losses, which are unavailable for commercial LLMs that expose only the final generated text. Recent black-box methods instead use word-recovery rate as the detection signal, but overlook that a word’s discriminative value can vary substantially across target models and target texts. To address this limitation, we propose ***PIRBD-PDD***, a target LLM- and text-adaptive framework for black-box pre-training data detection via *Prompt-Induced Recovery Behavior Decomposition*. ***PIRBD-PDD*** decomposes the target LLM’s recovery behavior into memorization-oriented and context-oriented modes through prompt induction, contrasts their recovery outcomes to identify high-discriminability words, and computes the final detection score from their recovery rate under the original, non-induced prompt. Experiments across diverse LLMs and data domains show that ***PIRBD-PDD*** consistently outperforms state-of-the-art black-box baselines. Further analyses provide empirical evidence for the proposed decomposition and show that high-discriminability words provide more robust and informative signals for pre-training data detection.