Data from the Transiting Exoplanet Survey Satellite (TESS) has produced of order one million light curves at cadences of 120 s and especially 1800 s for every ~27-day observing sector during its two-year nominal mission. These data constitute a treasure trove for the study of stellar variability and exoplanets. However, to fully utilize the data in such studies a proper removal of systematic noise sources must be performed before any analysis. The TESS Data for Asteroseismology (TDA) group is tasked with providing analysis-ready data for the TESS Asteroseismic Science Consortium, which covers the full spectrum of stellar variability types, including stellar oscillations and pulsations, spanning a wide range of variability timescales and amplitudes. We present here the two current implementations for co-trending of raw photometric light curves from TESS, which cover different regimes of variability to serve the entire seismic community. We find performance in terms of commonly used noise statistics to meet expectations and to be applicable to a wide range of different intrinsic variability types. Further, we find that the correction of light curves from a full sector of data can be completed well within a few days, meaning that when running in steady-state our routines are able to process one sector before data from the next arrives. Our pipeline is open-source and all processed data will be made available on TASOC and MAST.
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