As large language models (LLMs) increasingly rely on web-scale corpora, membership inference attacks (MIAs) have become essential tools for auditing unauthorized data usage. However, traditional token-level MIAs fail to generalize to large reasoning models (LRMs) due to data distribution shifts introduced during fine-tuning. While recent studies address this by encoding reasoning traces into latent semantic spaces, they sacrifice the interpretability strictly required for real-world copyright verification. In this paper, we demonstrate that an LRM’s internal memory states are explicitly leaked through its stylistic word choices. Our analysis reveals a distinct lexical dichotomy: non-member traces tend toward a "guessing-like" tone, whereas member traces exhibit a "remember-like" style. Motivated by this interesting phenomenon, we propose TraceMIA, an interpretable MIA framework that audits training corpora by computing membership scores based on the relative frequencies of discriminative cue words. Extensive empirical evaluations across representative LRMs and diverse datasets demonstrate that TraceMIA achieves robust detection efficacy while providing the transparent, human-readable evidence critical for practical auditing scenarios.