The Orion BN/KL complex is the nearest site of ongoing high-mass star formation. Recent proper motion observations provide convincing evidence of a recent (about 500 years ago) dynamical interaction between two massive young stellar objects (YSOs) in the region resulting in high velocities: the BN object and radio Source I. At the same time, Source I is surrounded by a nearly edge-on disc with radius ∼50 au. These two observations taken together are puzzling: a dynamical encounter between multiple stars naturally yields the proper motions, but the survival of a disc is challenging to explain. In this paper we take the first steps to numerically explore the preferred dynamical scenario of Goddi et al., in which Source I is a binary that underwent a scattering encounter with BN, in order to determine if a pre-existing disc can survive this encounter in some form. Treating only gravitational forces, we are able to thoroughly and efficiently cover a large range of encounter parameters. We find that disc material can indeed survive a three-body scattering event if (1) the encounter is close, i.e. BN’s closest approach to Source I is comparable to Source I’s semimajor axis and (2) the interplay of the three stars is of a short duration. Furthermore, we are able to constrain the initial conditions that can broadly produce the orientation of the present-day system’s disc relative to its velocity vector. To first order we can thus confirm the plausibility of the scattering scenario of Goddi et al., and we have significantly constrained the parameters and narrowed the focus of future, more complex and expensive attempts to computationally model the complicated BN/KL region.