  The gamma-ray Fermi-LAT Galactic centre excess (GCE) has puzzled scientists
for over 15 years. Despite ongoing debates about its properties, and especially
its spatial distribution, its nature remains elusive. We scrutinize how the
estimated spatial morphology of this excess depends on models for the Galactic
diffuse emission, focusing particularly on the extent to which the Galactic
plane and point sources are masked. Our main aim is to compare a spherically
symmetric morphology - potentially arising from the annihilation of dark matter
(DM) particles - with a boxy morphology - expected if faint unresolved sources
in the Galactic bulge dominate the excess emission. Recent claims favouring a
DM-motivated template for the GCE are shown to rely on a specific Galactic
bulge template, which performs worse than other templates for the Galactic
bulge. We find that a non-parametric model of the Galactic bulge derived from
the VVV survey results in a significantly better fit for the GCE than
DM-motivated templates. This result is independent of whether a GALPROP-based
model or a more non-parametric ring-based model is used to describe the diffuse
Galactic emission. This conclusion remains true even when additional freedom is
added in the background models, allowing for non-parametric modulation of the
model components and substantially improving the fit quality. When adopted,
optimized background models provide robust results in terms of preference for a
boxy bulge morphology of the GCE, regardless of the mask applied to the
Galactic plane.
