  Observing Earth-like exoplanets orbiting within the habitable zone of
Sun-like stars and studying their atmospheres in reflected starlight requires
contrasts of $\sim1\mathrm{e}{-10}$ in the visible. At such high contrast,
starlight reflected by exozodiacal dust is expected to be a significant source
of contamination. Here, we present high-fidelity simulations of coronagraphic
observations of a synthetic Solar System located at a distance of 10 pc and
observed with a 12 m and an 8 m circumscribed aperture diameter space telescope
operating at 500 nm wavelength. We explore different techniques to subtract the
exozodi and stellar speckles from the simulated images in the face-on, the 30
deg inclined, and the 60 deg inclined case and quantify the remaining
systematic noise as a function of the exozodiacal dust level of the system. We
find that in the face-on case, the exozodi can be subtracted down to the photon
noise limit for exozodi levels up to $\sim1000$ zodi using a simple toy model
for the exozodiacal disk, whereas in the 60 deg inclined case this only works
up to $\sim50$ zodi. We also investigate the impact of larger wavefront errors
and larger system distance, finding that while the former have no significant
impact, the latter has a strong (negative) impact. Ultimately, we derive a
penalty factor as a function of the exozodi level and system inclination that
should be considered in exoplanet yield studies as a realistic estimate for the
excess systematic noise from the exozodi.
