We study pairing in low-density neutron matter including the screening interaction due to the exchange of particle-hole and RPA excitations. As bare force, we employ the effective low-momentum interaction Vlowk, while the Fermi-liquid parameters are taken from a phenomenological energy density functional (SLy4) which correctly reproduces the equation of state of neutron matter. At low density, we find screening, i.e., pairing is reduced, while at higher densities, we find antiscreening, i.e., pairing is enhanced. This enhancement is mostly due to the strongly attractive Landau parameter f0. We discuss in detail the critical temperature Tc in the limit of low densities and show that the suppression of Tc predicted by Gor'kov and Melik-Barkhudarov can only be reproduced if the cutoff of the Vlowk interaction is scaled with the Fermi momentum. We also discuss the effect of noncondensed pairs on the density dependence of Tc in the framework of the Nozières-Schmitt-Rink theory. © 2018 American Physical Society.