  The high-frequency quasi-periodic oscillations (HFQPOs) that punctuate the
light curves of X-ray binary systems present a window onto the intrinsic
properties of stellar-mass black holes and hence a testbed for general
relativity. One explanation for these features is that relativistic distortion
of the accretion disc's differential rotation creates a trapping region in
which inertial waves (r-modes) might grow to observable amplitudes. Local
analyses, however, predict that large-scale magnetic fields push this trapping
region to the inner disc edge, where conditions may be unfavorable for r-mode
growth. We revisit this problem from a pseudo-Newtonian but fully global
perspective, deriving linearized equations describing a relativistic,
magnetized accretion flow, and calculating normal modes with and without
vertical density stratification. In an unstratified model, the choice of
vertical wavenumber determines the extent to which vertical magnetic fields
drive the r-modes toward the inner edge. In a global model fully incorporating
density stratification, we confirm that this susceptibility to magnetic fields
depends on disc thickness. Our calculations suggest that in thin discs, r-modes
may remain independent of the inner disc edge for vertical magnetic fields with
plasma betas as low as $\beta\approx 100-300$. We posit that the appearance of
r-modes in observations may be more determined by a competition between
excitation and damping mechanisms near the ISCO than the modification of the
trapping region by magnetic fields.
