tl;dr: Compared to Earth, the atmosphere on Mars is very thin; in addition, it contains much less of oxygen and water (i.e., is very dry). It is much colder there. These conditions may slow down oxidation to an irrelevant rate.
For an object of pure iron, note that according to the English Wikipedia about Mars:
"The atmosphere of Mars consists of about 96% carbon dioxide, 1.93%
argon and 1.89% nitrogen along with traces of oxygen and water."
This contributes as plausible contribution for a lesser rate of oxidation than on earth because the concentration of an oxidizer (i.e., oxygen) is much lower (0.146 vol%, according to the side table, ibid.) if one assumes absence of processes splitting the $\ce{CO2}$ to yield oxygen. To set these values into context (entry Earth):
"A dry atmosphere is composed of 78.084% nitrogen, 20.946% oxygen,
0.934% argon, and trace amounts of carbon dioxide and other gaseous molecules. [...] Water vapor content varies between 0.01% and 4% but averages about 1%."
Equally note that the reported surface temperatures on Mars (min 130 K, mean 210 K, max 308 K) are substantially lower, than on Earth (min 184 K, mean 287.16 K, max 330 K) -- equally slowing oxidation.
About water and atmosphere humidity: Provided the meteorites get water wetted, said perchlorates could start to work as oxidizer of iron. In comparison to this, dry perchlorate will remain inactive. Again, Mars' atmosphere (0.0210 vol% of water vapour, ibid.) seems to be considerably more conservative than Earth's.
You can't have oxidation alone, it is a electrochemical process where some other material in contact with the one oxidized has to be reduced. Corrosion of the meteorites equally could occur if these simultaneously contain grains of metals / alloys differing in the their electrode potential provided
these grains were in close contact with each other, especially if their grain boundary were water wetted, and
if one of the metals / alloys -- relatively speaking -- would be «less noble», i.e. a material with a more negative reduction potential, than any other grain / material in contact. The less noble grain than would become a galvanic anode and eventually be "eaten away", protecting the other, more noble one, to be oxidized.(table) The formation of these little, local electrochemical cells could be even more important if there were salty water droplets on the surface at room temperature and above accelerating corrosion. (This, by the way, a reason why steel bridges and copper house roofs exposed to the climate and atmosphere of salty seas are more prone to galvanic corrosion than similar constructions only exposed to fresh water.) Presence of phosphates in said meteorites however could slow down the oxidation of the meteorites (passivation, as assumed for the Iron pillar in Dehli).
Note: The initial answer assumed iron meteorites to contain discrete grains, occasionally altogether with grains of other metals. A comment by@KenFabian
pointed out iron meteorites however mainly consist of (Fe,Ni) alloys. Their electrochemical properties may be different to their components (e.g, table), which the edit aims to include.
@John
referred to pictures like «A rare pseudo-scalenohedral crystal habit» en.wikipedia.org/wiki/Hematite (the entry equally mentiones its use as jewelery as well as occurences on Mars), the title picture for the Czech (cs.wikipedia.org/wiki/Hematit) and Spanish (es.wikipedia.org/wiki/Hematita) wikipedia of $\ce{Fe2O3}$, or the «Perfekt gewachsener Hämatit-Skalenoeder von der Insel Hormus, Iran » on de.wikipedia.org/wiki/Hämatit of high reflectance but still share the rust-red streak. $\endgroup$