The gamma-ray Fermi-LAT Galactic centre excess (GCE) has puzzled scientists for over 15 years. Despite ongoing debates about its properties, especially its spatial distribution, its nature remains elusive. This study investigates how the estimated spatial morphology of the GCE depends on models for the Galactic diffuse emission, focusing on the extent to which the Galactic plane and point sources are masked. The main aim is to compare a spherically symmetric morphology—potentially arising from dark matter (DM) particle annihilation—with a boxy morphology—expected if faint unresolved sources in the Galactic bulge dominate the excess emission. Recent claims favoring a DM-motivated template for the GCE rely on a specific Galactic bulge template, which performs worse than other templates. 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 GALPR0P-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 for the GCE, regardless of the mask applied to the Galactic plane. The GCE may be due to an unresolved population of, for example, millisecond pulsars (MSPs), stellar remnants associated with the central stellar population of the Milky Way. However, there is debate on whether more GC MSPs should be resolved and whether there are sufficient corresponding low mass X-ray binary (LMXB) systems. One method to distinguish between the MSP and DM proposals is whether the GCE has a spherical morphology or follows the bulge-like morphology of the GC's stellar populations. The main obstacle to accurately determining the GCE morphology is uncertainties in the Galactic diffuse emission. When residuals in the gamma-ray fit were significantly reduced through advanced gas models or new fitting techniques, a strong preference for the excess tracing old stars in the Galactic bulge emerged. However, recent claims have made opposite claims. Another way to distinguish between the DM and MSP explanations is to look for non-Poissonian statistics in the GCE, which would indicate the MSP explanation. However, this is more susceptible to uncertainties in the Galactic diffuse emission. New analyses using methodological developments that reduce the impact of Galactic diffuse emission modelling systematics found a sizable contribution from faint, sub-threshold point sources to the GCE. Accounting for uncertainties in the Galactic diffuse emission model is key to making robust inferences on the Fermi GCE properties and overcoming the so-called "reality gap" between models and real data. Different solutions were explored to overcome systematics related to the Galactic diffuse emission modelling. These approaches either rely on input from cosmic-ray propagation codes like GALPROP orThe gamma-ray Fermi-LAT Galactic centre excess (GCE) has puzzled scientists for over 15 years. Despite ongoing debates about its properties, especially its spatial distribution, its nature remains elusive. This study investigates how the estimated spatial morphology of the GCE depends on models for the Galactic diffuse emission, focusing on the extent to which the Galactic plane and point sources are masked. The main aim is to compare a spherically symmetric morphology—potentially arising from dark matter (DM) particle annihilation—with a boxy morphology—expected if faint unresolved sources in the Galactic bulge dominate the excess emission. Recent claims favoring a DM-motivated template for the GCE rely on a specific Galactic bulge template, which performs worse than other templates. 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 GALPR0P-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 for the GCE, regardless of the mask applied to the Galactic plane. The GCE may be due to an unresolved population of, for example, millisecond pulsars (MSPs), stellar remnants associated with the central stellar population of the Milky Way. However, there is debate on whether more GC MSPs should be resolved and whether there are sufficient corresponding low mass X-ray binary (LMXB) systems. One method to distinguish between the MSP and DM proposals is whether the GCE has a spherical morphology or follows the bulge-like morphology of the GC's stellar populations. The main obstacle to accurately determining the GCE morphology is uncertainties in the Galactic diffuse emission. When residuals in the gamma-ray fit were significantly reduced through advanced gas models or new fitting techniques, a strong preference for the excess tracing old stars in the Galactic bulge emerged. However, recent claims have made opposite claims. Another way to distinguish between the DM and MSP explanations is to look for non-Poissonian statistics in the GCE, which would indicate the MSP explanation. However, this is more susceptible to uncertainties in the Galactic diffuse emission. New analyses using methodological developments that reduce the impact of Galactic diffuse emission modelling systematics found a sizable contribution from faint, sub-threshold point sources to the GCE. Accounting for uncertainties in the Galactic diffuse emission model is key to making robust inferences on the Fermi GCE properties and overcoming the so-called "reality gap" between models and real data. Different solutions were explored to overcome systematics related to the Galactic diffuse emission modelling. These approaches either rely on input from cosmic-ray propagation codes like GALPROP or