The influence of single-neutron stripping on the near-barrier elastic scattering angular distributions for the 6,8 He + 208 Pb systems is investigated through coupled reaction channels (CRC) calculations fitting recently published data to explore the differences in the absorptive potential found in the scattering of these two neutronrich nuclei. The inclusion of the coupling reduces the elastic cross section in the Coulomb-nuclear interference region for 8 He scattering, whereas for 6 He its major impact is on the large-angle elastic scattering. The real and imaginary dynamic polarization potentials are obtained by inverting the CRC elastic scattering S-matrix elements. These show that the main absorptive features occur between 11 and 12 fm for both projectiles, while the attractive features are separated by about 1 fm, with their main structures occurring at 10.5 fm for 6 He and 11.5 fm for 8 He.