  Next generation gravitational waves (GWs) observatories are expected to
measure GW signals with unprecedented sensitivity, opening new, independent
avenues to learn about our Universe. The distance-redshift relation is a
fulcrum for cosmology and can be tested with GWs emitted by merging binaries of
compact objects, called standard sirens, thanks to the fact that they provide
the absolute distance from the source. On the other hand, fluctuations of the
intervening matter density field induce modifications on the measurement of
luminosity distance compared to that of a homogeneous universe. Assuming that
the redshift information is obtained through the detection of an
electromagnetic counterpart, we investigate the impact that lensing of GWs
might have in the inference of cosmological parameters. We treat lensing as a
systematic error and check for residual bias on the values of the cosmological
parameters. We do so by means of mock catalogues of bright sirens events in
different scenarios relevant to Einstein Telescope. For our fiducial scenario,
the lensing bias can be comparable to or greater than the expected statistical
uncertainty of the cosmological parameters, although non-negligible
fluctuations in the bias values are observed for different realisations of the
mock catalogue. We also discuss some mitigation strategies that can be adopted
in the data analysis. Overall, our work highlights the need to model lensing
effects when using standard sirens as probes of the distance-redshift relation.
