There were a lot of orbiters sent to Mars already.
From all the Mars orbiters which one had the lowest altitude?
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Depending how you count, possibly Viking two which started from 302 km low point and was predicted to de-orbit sometime after 2019. So it either already passed through a a lowest possible and now an orbiter on the surface of mars (technically a height of zero), or at this time (December 2020) in a very low and decreasing orbit somewhere around 150 km.
More seriously some digging around gets:
Maven has operated down to 150km
MRO is listed as sustaining around 250km
Mars Express around 298
mars Odyssey around 400
The Indian Mars Orbiter is listed as at Periareon of 421 km
The nature of orbits, aerobraking and the science gains from low altitude operation probably means 'current lowest' trades off at various times among the various probes at around the 150km mark which seems to be the lowest reasonably stable orbit height as they have been allowed to decay due to atmospheric drag and then been reboosted to target various science or rover support operations. Operating lower gets more science (or better rover uplink), but needs more fuel so reduces total mission time at mars. Suspect some complex trade offs involved here that mean the true answer will be in flux.