  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 (T'DA) 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.
