  Although the main goal of the Transiting Exoplanet Survey Satellite
(\textit{TESS}) is to search for new transiting exoplanets, its data can also
be used to study in further detail already known systems. The \textit{TESS}
bandpass is particularly interesting to study the limb-darkening effect of the
stellar host which is imprinted in transit lightcurves, as the widely used
\textsc{phoenix} and \textsc{atlas} stellar models predict different
limb-darkening profiles. Here we study this effect by fitting the transit
lightcurves of 176 known exoplanetary systems observed by \textit{TESS}, which
allows us to extract empirical limb-darkening coefficients (LDCs) for the
widely used quadratic law, but also updated transit parameters (including
ephemerides refinements) as a byproduct. Comparing our empirically obtained
LDCs with theoretical predictions, we find significant offsets when using
tabulated \textit{TESS} LDCs. Specifically, the $u_2$ coefficients obtained
using \textsc{phoenix} models show the largest discrepancies depending on the
method used to derive them, with offsets that can reach up to $\Delta u_2
\approx 0.2$ on average. Most of those average offsets disappear, however, if
one uses the SPAM algorithm introduced by Howarth (2011) to calculate the LDCs
instead. Our results suggest, however, that for stars cooler than about 5000 K,
no methodology is good enough to explain the limb-darkening effect: we observe
a sharp deviation between measured and predicted LDCs on both quadratic LDCs of
order $\Delta u_1, \Delta u_2 \approx 0.2$ for those cool stars. We recommend
caution when assuming limb-darkening coefficients as perfectly known thus, in
particular for these cooler stars when analyzing \textit{TESS} transit
lightcurves.
