  In Khadka et al. (2023), a sample of X-ray-detected reverberation-mapped
quasars was presented and applied for the comparison of cosmological
constraints inferred using two well-established relations in AGN -- the
X-ray/UV luminosity ($L_{X}-L_{UV}$) relation and the broad-line region
radius-luminosity ($R-L$) relation. $L_{X}-L_{UV}$ and $R-L$ luminosity
distances to the same quasars exhibit a distribution of their differences that
is generally asymmetric and positively shifted for the six cosmological models
we consider. We demonstrate that this behaviour can be interpreted
qualitatively to arise as a result of the dust extinction of UV/X-ray quasar
emission. We show that the extinction always contributes to the non-zero
difference between $L_{X}-L_{UV}$-based and $R-L$-based luminosity distances
and we derive a linear relationship between the X-ray/UV colour index
$E_{X-UV}$ and the luminosity-distance difference, which also depends on the
value of the $L_{X}-L_{UV}$ relation slope. Taking into account the median and
the peak values of the luminosity-distance difference distributions, the
average X-ray/UV colour index falls in the range of
$\overline{E}_{X-UV}=0.03-0.28$ mag for the current sample of 58 sources. This
amount of extinction is typical for the majority of quasars and it can be
attributed to the circumnuclear and interstellar media of host galaxies. After
applying the standard hard X-ray and far-UV extinction cuts, heavily extincted
sources are removed but overall the shift towards positive values persists. The
effect of extinction on luminosity distances is more pronounced for the
$L_{X}-L_{UV}$ relation since the extinction of UV and X-ray emissions both
contribute.
