Thermostatically Controlled Load (TCL) is an important flexible resource that can participate in microgrid demand response and facilitate renewable energy integration. However, missing TCL energy consumption data caused by sensor failures, communication interruptions, and other operational uncertainties may lead to inaccurate load characteristic identification, thereby reducing the accuracy of aggregated modeling and optimal microgrid scheduling. To address this issue, an Improved Copy-Paste Imputation (ICPI) method based on multi-feature fusion is proposed. The proposed method reconstructs missing TCL energy consumption data by establishing a composite similarity coefficient that integrates weekly characteristics, seasonal characteristics, extreme-value characteristics, and load profile correlation. Based on the reconstructed data, an aggregated TCL virtual battery model is developed and incorporated into a microgrid optimal scheduling framework, achieving coordinated data reconstruction, load aggregation modeling, and scheduling optimization. Simulation results demonstrate that the proposed ICPI method outperforms conventional imputation approaches in terms of both mean absolute percentage error and normalized root mean square error. Moreover, the reconstructed data effectively mitigate the adverse effects of missing data on microgrid scheduling, thereby improving the economic performance and operational stability of the system. The proposed framework provides an effective solution for integrating flexible loads into optimal microgrid scheduling under incomplete data conditions.