  It is possible to explain the discrepancy (tension) between the local
measurement of the cosmological parameter $H_0$ (the Hubble constant) and its
value derived from the Planck-mission measurements of the Cosmic Microwave
Background (CMB) by considering contamination of the CMB by emission from some
medium surrounding distant extragalactic sources (a distant foreground), such
as extremely cold coarse-grain (grey) dust. As any other foreground, it would
alter the CMB power spectrum and contribute to the dispersion of CMB
temperature fluctuations. By generating random samples of CMB with different
dispersions, we have checked that the increased dispersion leads to a smaller
estimated value of $H_0$, the rest of the cosmological model parameters
remaining fixed. This might explain the reduced value of the {\it
Planck}-derived parameter $H_0$ with respect to the local measurements. The
cold grey dust for some time has been suspected to populate intergalactic space
and it is known to be almost undetectable, except for the effect of dimming
remote extragalactic sources.
