Since - according to the OP's comment - this is a case of Scientists Behaving Badly (and not state-sponsored warfare) on both sides, we can presume that neither side would want to involve Earth, as to do so would undoubtedly result in their being told in no uncertain terms to stop their foolish nonsense, and would probably then lead to their being removed, replaced and prosecuted if they persisted - and survived.
So, these badly-behaving scientist types must rely on the equipment and supplies that they have on hand. Being scientists and nerdy-types, they would most likely rely on any drones or other remote-controlled equipment before thinking of getting physical in person. If they didn't have explosives already (which is unlikely), the base chemists could undoubtedly brew some up, and from there, the engineers could build perfectly effective bombs, enhanced with spare metal items that would act as shrapnel. Given that we have engineer and physicist types, we could even expect crude Explosively-Formed-Penetrators, which are anything but crude in their ability to deliver damage at a fair distance. Drones could drop bombs if they can fly (not out of the question even if Mars' atmosphere is thinner than Earth's), or could fire rockets which may also be improvised.
On the defensive side, there are probably reconnaissance satellites, though they could be a two-edged sword. The scientists will know that they are behaving badly, and may want to hide the evidence of their wrongdoing, and deliberately operate in any gaps in the satellite coverage so that they won't have to make suspicious edits or deletions to the satellite feed recordings. On the other hand, they may also try to stage-manage being "surprised" by the other side's attack, but that would then beg the question as to how they were able to retaliate effectively on such short notice.
A likely possibility is for the scientists to make use of the reconnaissance satellites, and to cause "battle damage" to the satellite feed recording media themselves in the aftermath, providing that the satellites don't connect directly to Earth too - which it entirely likely. However, Line-of-Sight matters in interplanetary communications, and the attacks would likely be scheduled for a time when the links to Earth were down - i.e. local night-time.
However, reconnaissance satellites may not be that effective a tool. Without software to track the movement of manmade objects (which may not be included in an essentially non-military operation as anyone going out would likely file their travel plans and broadcast their location at all times), spotting something as small as a drone could be quite difficult. Given the amount of land area, spotting another drone using drone cameras would likely not happen except when an attacking drone came quite close to its objective.
Given the logistics of leaving their habitats and travelling to make war on their enemies, it is only more likely that both sides will try to conduct the battle remotely rather than in person.
Drones may be fitted with simple weaponry such as nail guns or shrapnel bombs in order to deal with other drones, but given the distances involved, it is likely that these will be of limited effectiveness, and that much of their ammunition will be expended to little effect, or they will be single-use items, destroying themselves along with their target.
Finally, given that Mars' surface is a hostile environment, we can expect that the scientists would all suit up before the fighting started, and if their habitats did suffer damage, many of them would survive, environment suits by necessity being quite tough, and likely only being fatally compromised by a direct hit or a unfortunate mischance.
All in all, with both sides attacking the other, and the difficulties of defending effectively as opposed to successfully attacking, we can expect that both sides will achieve their goal of causing damage to the other side's habitat, and for there to be relatively few human casualties or fatalities.
After the battle, the survivors will be pre-occupied with patching up their habitats, recovering any salvageable equipment, and treating the injured. They may try to hide it, but the authorities will probably figure out fairly soon that there has been an incident that neither side really wants to talk about, or is being evasive about, and a well-armed investigatory mission will be scrambled.
In the time before the investigatory mission arrives, there may be further attacks, probably of decreasing effectiveness as the scientists attempt to make use of their dwindling resources.
So, after the battle(s) and the reconstruction, there will likely be a lot of survivors on both sides who will then have to either hide the fact that they went to war against the other side without authorisation, or claim self-defence. All things considered, we can expect that the investigatory teams won't buy into the scientist's arguments against the other side, and for there to be prosecutions...
