This work introduces the first framework for reconstructing surgical dialogue from unstructured real-world recordings, which is crucial for characterizing teaching tasks. In surgical training, the formative verbal feedback that trainers provide to trainees during live surgeries is crucial for ensuring safety, correcting behavior immediately, and facilitating long-term skill acquisition. However, analyzing and quantifying this feedback is challenging due to its unstructured and specialized nature. Automated systems are essential to manage these complexities at scale, allowing for the creation of structured datasets that enhance feedback analysis and improve surgical education. Our framework integrates voice activity detection, speaker diarization, and automated speech recaognition, with a novel enhancement that 1) removes hallucinations (non-existent utterances generated during speech recognition fueled by noise in the operating room) and 2) separates speech from trainers and trainees using few-shot voice samples. These aspects are vital for reconstructing accurate surgical dialogues and understanding the roles of operating room participants. Using data from 33 real-world surgeries, we demonstrated the system's capability to reconstruct surgical teaching dialogues and detect feedback instances effectively (F1 score of 0.79+/-0.07). Moreover, our hallucination removal step improves feedback detection performance by ~14%. Evaluation on downstream clinically relevant tasks of predicting Behavioral Adjustment of trainees and classifying Technical feedback, showed performances comparable to manual annotations with F1 scores of 0.82+/0.03 and 0.81+/0.03 respectively. These results highlight the effectiveness of our framework in supporting clinically relevant tasks and improving over manual methods.