Aims. We investigate a possible close encounter between M33 and M31 in the past to understand the role of galaxy-galaxy interactions in shaping the matter distribution in galaxy outskirts. Methods. By examining a variety of initial conditions, we recovered possible orbital trajectories of M33, M31, and the Milky Way in the past, which are compatible with the Early Third Data Release of the Gaia mission and with mass estimates of Local Group spirals. Using test-particle simulations, we explored if the M33 warp and its dark satellite distribution have been induced by a past M33–M31 encounter along these orbits, after tuning mass losses and the dynamical friction term with the help of N-body numerical simulations. Results. A close encounter of M33 and M31 in the past has a low but non-negligible probability. If the two galaxies had been closer in the past, their minimum distance would be of the order of 100 kpc or larger, and this happened earlier than 3 Gyr ago. During this encounter, 35–40% of the dark matter mass of M33 might have been removed from the halo due to tidal stripping. A detailed comparison of the results of test-particle simulations with the observed disk warp or with the spatial distribution of candidate dark satellites of M33 suggests that a closer passage of M33 around M31 cannot, however, be responsible for the observed morphological features. We suggest that more recent gas accretion events, possibly from a cosmic filament, might cause the misalignment of the outer disk of M33 after the rapid inner disk formation.