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The Polarized Instrument for Long-wavelength Observation of the Tenuous interstellar medium (PILOT) is a balloon-borne experiment that aims to measure the polarized emission of thermal dust at a wavelength of 240 um (1.2 THz). The PILOT experiment flew from Timmins, Ontario, Canada in 2015 and 2019 and from Alice Springs, Australia in April 2017. The in-flight performance of the instrument during the second flight was described in Mangilli et al. 2019. In this paper, we present data processing steps that were not presented in Mangilli et al. 2019 and that we have recently implemented to correct for several remaining instrumental effects. The additional data processing concerns corrections related to detector cross-talk and readout circuit memory effects, and leakage from total intensity to polarization. We illustrate the above effects and the performance of our corrections using data obtained during the third flight of PILOT, but the methods used to assess the impact of these effects on the final science-ready data, and our strategies for correcting them will be applied to all PILOT data. We show that the above corrections, and in particular that for the intensity to polarization leakage, which is most critical for accurate polarization measurements with PILOT, are accurate to better than 0.4 % as measured on Jupiter during flight#3.