It is possible to explain the discrepancy (tension) between the local measurement of the cosmological parameter H0 (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, such as
extremely cold coarse-grain (grey) dust. Though being distant, such a medium would still be in the foreground with respect
to the CMB, and, as any other foreground, it would alter the CMB power spectrum. This could 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 H0, the rest of the cosmological model parameters remaining
fixed. This might explain the reduced value of the Planck-derived parameter H0 with respect to the local measurements.