Repairing incomplete trajectory data is essential for downstream spatio-temporal applications. Yet, existing repair methods focus solely on reconstruction without documenting the reasoning behind repair decisions, undermining trust in safety-critical applications where repaired trajectories affect operational decisions, such as in maritime anomaly detection and route planning. We introduce repair provenance - structured, queryable metadata that documents the full reasoning chain behind each repair - which transforms imputation from pure data recovery into a task that supports downstream decision-making. We propose VISTA (knowledge-driven interpretable vessel trajectory imputation), a framework that reliably equips repaired trajectories with repair provenance by grounding LLM reasoning in data-verified knowledge. Specifically, we formalize Structured Data-derived Knowledge (SDK), a knowledge model whose data-verifiable components can be validated against real data and used to anchor and constrain LLM-generated explanations. We organize SDK in a Structured Data-derived Knowledge Graph (SD-KG) and establish a data-knowledge-data loop for extraction, validation, and incremental maintenance over large-scale AIS data. A workflow management layer with parallel scheduling, fault tolerance, and redundancy control ensures consistent and efficient end-to-end processing. Experiments on two large-scale AIS datasets show that VISTA achieves state-of-the-art accuracy, improving over baselines by 5-91% and reducing inference time by 51-93%, while producing repair provenance, whose interpretability is further validated through a case study and an interactive demo system.