Abstract We revisit the orbital history of the Triangulum galaxy (M33) around the Andromeda galaxy (M31) in view of the recent Gaia Data Release 2 proper motion measurements for both Local Group galaxies. Earlier studies consider highly idealised dynamical friction, but neglect the effects of dynamical mass loss. We show the latter process to be important using mutually consistent orbit integration and N-body simulations. Following this approach we find an orbital solution that brings these galaxies to within ∼50 kpc of each other in the past, ∼6.5 Gyr ago. We explore the implications of their interaction using an N-body/hydrodynamical simulation with a focus on the origin of two prominent features: 1) M31’s Giant Stellar Stream; and 2) the M31-M33 H i filament. We find that the tidal interaction does not produce a structure reminiscent of the stellar stream that survives up to the present day. In contrast, the M31-M33 H i filament is likely a fossil structure dating back to the time of the ancient encounter between these galaxies. Similarly, the observed outer disc warp in M33 may well be a relic of this past event. Our model suggests the presence of a tidally induced gas envelope around these galaxies, and the existence of a diffuse gas stream, the ‘Triangulum stream’, stretching for tens of kpc from M33 away from M31. We anticipate upcoming observations with the recently commissioned, Five-hundred-meter Aperture Spherical radio Telescope (FAST) that will target the putative stream in its first years of operation.