We address in this work the instrumental systematic errors that can potentially affect the forthcoming and future Cosmic Microwave Background experiments aimed at observing its polarized emission. In particular, we focus on the systematics induced by the beam and calibration, which are considered the major sources of leakage from total intensity measurements to polarization. We simulated synthetic data sets with Time-Ordered Astrophysics Scalable Tools, a publicly available simulation and data analysis package. We also propose a mitigation technique aiming at reducing the leakage by means of a template fitting approach. This technique has shown promising results reducing the leakage by 2 orders of magnitude at the power spectrum level when applied to a realistic simulated data set of the LiteBIRD satellite mission.