Wireless digital twins can be leveraged to provide site-specific synthetic channel information through precise physical modeling and signal propagation simulations. This can help reduce the overhead of channel state information (CSI) acquisition, particularly needed for large-scale MIMO systems. For high-quality digital twin channels, the classical approach is to increase the digital twin fidelity via more accurate modeling of the environment, propagation, and hardware. This, however, comes with high computational cost, making it unsuitable for real-time applications. In this paper, we propose a new framework that, instead of calibrating the digital twin model itself, calibrates the DFT-domain channel information to reduce the gap between the low-fidelity digital twin and its high-fidelity counterpart or the real world. This allows systems to leverage a low-complexity digital twin for generating real-time channel information without compromising quality. To evaluate the effectiveness of the proposed approach, we adopt codebook-based CSI feedback as a case study, where refined synthetic channel information is used to identify the most relevant DFT codewords for each user. Simulation results demonstrate the effectiveness of the proposed digital twin calibration approach in achieving high CSI acquisition accuracy while reducing the computational overhead of the digital twin. This paves the way for realizing digital twin assisted wireless systems.