  Galaxies within galaxy clusters are known to be subject to a wide variety of
environmental effects, both gravitational and hydrodynamical. In this study, we
examine the purely gravitational interaction of idealised galaxy models falling
into a galaxy cluster in the context of Modified Newtonian Dynamics (MOND).
This modification of gravity gives rise to an external field effect (EFE),
where the internal dynamics of a system are affected by the presence of
external gravitational fields. We examine the consequences of the EFE on low
and high mass disk galaxies in time-evolving analytic background cluster
potentials, considering orbits with weak and strong tidal fields. By varying
the orbital plane of the galaxies we also test the effect of having the tidal
interaction orthogonal or parallel to the disk. Furthermore, we consider as a
control sample models where the EFE has been removed and they are only affected
by tides. Our results suggest that MOND cluster galaxies should exhibit clear
asymmetries in their isophotes, suffer increased mass loss and a reduction in
their rotation curves due to the combined effect of cluster tides and the
external field. In particular, low mass galaxies are hit hard by the EFE,
becoming dominated by dispersion rather than rotation even in the absence of
tides.
