  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. 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, after tuning mass losses and the dynamical friction term with the help
of N-body numerical simulations. 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.
