Digital twins (DTs) enable powerful predictive analytics, but persistent discrepancies between simulations and real systems--known as the reality gap--undermine their reliability. Coined in robotics, the term now applies to DTs, where discrepancies stem from context mismatches, cross-domain interactions, and multi-scale dynamics. Among these, context mismatch is pressing and underexplored, as DT accuracy depends on capturing operational context, often only partially observable. However, DTs have a key advantage: simulators can systematically vary contextual factors and explore scenarios difficult or impossible to observe empirically, informing inference and model alignment. While sim-to-real transfer like domain adaptation shows promise in robotics, their application to DTs poses two key challenges. First, unlike one-time policy transfers, DTs require continuous calibration across an asset's lifecycle--demanding structured information flow, timely detection of out-of-sync states, and integration of historical and new data. Second, DTs often perform inverse modeling, inferring latent states or faults from observations that may reflect multiple evolving contexts. These needs strain purely data-driven models and risk violating physical consistency. Though some approaches preserve validity via reduced-order model, most domain adaptation techniques still lack such constraints. To address this, we propose a Reality Gap Analysis (RGA) module for DTs that continuously integrates new sensor data, detects misalignments, and recalibrates DTs via a query-response framework. Our approach fuses domain-adversarial deep learning with reduced-order simulator guidance to improve context inference and preserve physical consistency. We illustrate the RGA module in a structural health monitoring case study on a steel truss bridge in Pittsburgh, PA, showing faster calibration and better real-world alignment.