  We comment on the paper of S. Postnikov et al. in Phys. Rev. D 82, 024016
(2010) and give a modified formula that needs to be taken into account when
calculating the tidal Love number of neutron stars in case a first order
phase-transition occurs at non-zero pressure. We show that the error made when
using the original formula tends to zero as $p \rightarrow 0$ and we estimate
the maximum relative error to be $\sim 5\%$ if the density discontinuity is at
larger densities.
