I always wonder where Tech-Marines stand re: divided loyalties.
Does Mars know about the Grey Knights?
Well, they have Techmarines of their own and their own mini-Forge World, Deimos, in orbit over Titan, and while the Grey Knights are known to mind-scrub almost everyone they leave alive, the Mechanicum never deletes anything. Even if they don't know their name, a Grey Knights-shaped void full of Dreadknights and Nemesis force weapons must remain in their logistical records, to say nothing of what their ubiquitous observatories can see literally in their own solar system.
So yes, Mars knows about the Grey Knights in the same putative way it knows about everything "secret": the information is there, even if they haven't bothered to upload an analysis of it into their consensus awareness because they're preoccupied with matters of greater import. As for how Techmarines handle their divided loyalties, I've always assumed they see Mars through the same lens they see the Imperial Cult: a matter for baseline humans not specially marked out by the Emperor for martial greatness. They're technicians, after all, not magi, so Mars has no reason to disabuse them of that view.
Maybe it's just Abnett and McNeill's writing style, but I always got the distinct sense that the Mechanicum has been humoring the Imperium ever since the Treaty of Olympus in order to keep someone else between them and whatever alien/mutant/heretics might otherwise distract from the Quest for Knowledge, and much of the more obviously ludicrous ritual trappings are exclusively for their benefit. Certainly they don't seem to bother with many of them amongst themselves.