Ordo Grammaticus is one of the most peculiar branch of The Inquisition, specializing specifically in being the Imperium's pissed off auto-correct. That being said, they don't only underline your mistakes with red; they also like to shove parchment with said mistakes in your mouth and make you write the whole thing all over, which is especially painful with that red pen of theirs stuck firmly in your butt (or eye if you've made REALLY stupid mistake). They justify this sadistic behavior by saying that they pursue the Emperor's own dream of bringing humanity to perfection. That being said, they are especially touchy about religious scriptures, official documents, and decrees, etc. Another group they particularly dislike are people who imitate ork speech, as they consider this to be a figurative rape of the Gothic language and the old guardsmen argument that they are practicing to taunt orks in combat doesn't help these days, either - not to mention their downright bullying of lower-class peasants, some of whom don't even speak Gothic and are trying to contribute in their own way.
Forces in service of grammar
As other Ordos, Grammaticus too has its own loyal men-at-arms to enforce what they believe is the will of The Emperor himself - the Red Quills and the Erasers. Both are groups of Stormtroopers handpicked from Schola Progenia by Grammaticus Inquisitors for showing potential to be meticulous OCD-suffering little shits just like their possible future employers, and possibly even to rise through the ranks among them. This process keeps the Ordo supplied with experienced Inquisitors who could gladly spend an entire evening correcting EVERY SINGLE FUCKING SENTENCE YOU SAY (just kidding they usually last like 10 minutes tops before a red pen starts heading towards your anus/eye).
- Red Quills Red Quills are Inquisitorial bodyguards and essentially walking talking pencil cases (as Inquisitors usually need so much shit that Servo-skulls can't carry it all). They wear dark red carapace armor and red cloaks earning them the distinct nickname of Crimson Cunts. Of the two Stormtrooper forces mentioned, fewer people are likely to rise from their position in the Red Quills than in the Erasers. The reason for this is that since they got picked straight from the school desks to just yell at uneducated or just downright illiterate peasants like some fusion of Gordon Ramsay and an angry English teacher, they are likely to have their heads even further up their own asses than the Eldar and Red Scorpions combined. Since the goals of the Ordo Grammaticus are to serve The Imperium and its people in their own unique way, the Ordo considers most of them to be unfitting.
- The Erasers While their colleagues are tasked with following the Inquisitors around and licking their boots, the Erasers are those who actually get shit done. As in: all day every day workhorse tempo kind of getting shit done. They usually wear black armor and prefer lighter variants that offer more mobility in combat and some extra sneakiness. They are the Ordo's extended arm that fights against heretics that spread shitty, poorly written fanfic (watch the example only in case of wanting to get purged ) as well as ork-impersonating lower-hive gangsters (ever heard of Necromunda?). They also undergo special training that gives them some quite handy skills that turn them into a cross between your standard Stormtroopers and Vindicare Assassins. Their job makes them considerably tougher than the previously mentioned force and since they see the worst kind of shit their order can face on a daily basis, those few that survive often later become fully fledged Inquisitors. As for their name - that has further meaning than just their employer's love of office tools. Let's just say that some people's existence is so unnecessary and annoying that it's better for them to never have existed in the first place. I mean, have you heard about those Tzeench cultists who were spreading some poorly written fliers with daemon summoning instructions? Or that one guy who once called some local recruiting Space Marine Chaplain a SPEHSS MAHREEN? NO? You haven't? Good.
OK, ok for real now
...if you actually took all of the above seriously, then read up a little more on the subject (although some of it was based on reality). In the WH40k community people use the term Ordo Grammaticus for anyone who is essentially a grammar nazi. Although the latter term is more universal, Ordo Grammaticus is becoming more popular as a meme and as a fanfic trope that is starting to spawn new theories (more on that later).
To identify one in real life you don't have to look further than your daily WH40k Facebook or Twitter page's comments and watch some poor bastard, who probably doesn't even speak English correctly or got into 40k just recently eat it from every single butthurt neckbeard who is willing to jump on that brakeless Hatetrain. Of course, some may refer as such to people who just edit pages like me, and to people like that I would like to tell them to shut THEIR FUCKING HERESY-SPEWING WARP RIFTS THEY CALL THEIR MOUTHS BEFORE I TAKE THIS RED PEN AND... *INTERMISSION*
Theories and Stories
Fluff-wise there are several theories about things that the Ordo may have stuck their noses into and since not much is known about them and they deny most of that not much you're free to make up your own opinion, just make sure it stays your own if you know what's good for you.
The most notable theory says that, as Commander Mr. Clean was becoming the Jar Jar Binks of Dawn of War, the Ordo Grammaticus couldn't just watch as he desecrated the holy name of the Emperor and spread his foul manner of "speech" among his own Battle Brothers. The theory even goes as far as that they themselves sent Vance Motherfucking Stubbs to personally fuck his bald shit up and even that Cyrus was the one that provided him with the info to do so, being the sneaky bastard that he is. The theory even goes as far as saying that the loss of those 100 Baneblades was caused by a fucked up order on the Inquisition's part.
Grammaticus Space Marines?
Another theory suggests that the Ordo Grammaticus was supposed to get their very own Space Marine force as their Chamber Militant. They were supposed to be called The Correctors and were supposed to find all the heretical bullshit Lorgar wrote during the Horus Heresy and fight against his forces. There is even talk of a grand parade where all Grammaticus Inquisitors were supposed to greet their new personal super-soldiers, but a fatal mistake occurred. The banners the Astartes were holding all had the word "Corectors" spelled with only one r. The only other thing we know besides that is that a few days later a Magos Biologis received a cargo of Space Marine Geneseed from an unknown source.
A Note on Plausibility
One of the stranger aspects of life in the Imperium is that Low Gothic is so uniform across so many planets with such poor communication between them (the Imperium's *only* access to FTL communications is psykers, which civilians can't even legally observe using their powers), particularly since the setting is far too grimdark for state-sponsored education to ensure everyone learns the same language (outside of the Schola Progenium, of course, which does exactly that). As linguistic drift represents a significant threat to Imperial stability, it would hardly stretch the imagination for the Inquisition to declare it to be deeply heretical, and to have an Ordo dedicated to finding and eliminating anyone deliberately spreading it - although they would need much more manpower than any other Ordo to even begin to make a dent on preventing such drift from happening by accident.