We measure the gravitational lensing signal around satellite galaxies in a sample of galaxy clusters at z < 0.15 by combining high-quality imaging data from the Canada-France-Hawaii Telescope with a large sample of spectroscopically-confirmed cluster members. We use extensive image simulations to assess the accuracy of shape measurements of faint, background sources in the vicinity of bright satellite galaxies. We find a small but significant bias, as light from the lenses makes the shapes of background galaxies appear radially aligned with the lens. We account for this bias by applying a correction that depends on both lens size and magnitude. We also correct for contamination of the source sample by cluster members. We use a physically-motivated definition of subhalo mass, namely the mass bound to the subhalo, m bg , similar to definitions used by common subhalo finders in numerical simulations. Binning the satellites by stellar mass we provide a direct measurement of the subhalo-to-stellar-mass relation, log m bg /M = (11.54 ± 0.05) + (0.95 ± 0.10) log[m /(2 × 10 10 M )]. This best-fitting relation implies that, at a stellar mass m ∼ 3 × 10 10 M , subhalo masses are roughly 50 per cent of those of central galaxies, and this fraction decreases at higher stellar masses. We find some evidence for a sharp change in the total-to-stellar mass ratio around the clusters' scale radius, which could be interpreted as galaxies within the scale radius having suffered more strongly from tidal stripping, but remain cautious regarding this interpretation.