First off, Nephene Nep has an excellent answer to the question as stated.
For an additional perspective; say Angel Agnes is ordered to track down and destroy Demon Demarcus. If, when cornered, Demarcus threatens to go loud, Agnes should reply an unironic "I don't care." If Agnes deliberately aborts her mission because she feels it would endanger the GM, then Agnes has Fallen, and an Angel more willing to blindly follow its orders will attend to her shortly.
I'd also encouraging the question of the assumption
...the GM itself wants to remain hidden.
The GM certainly doesn't want its Infrastructure interrupted by bumbling insects, but "remaining hidden" isn't an active priority of it, even though it obfuscates its parts and actions.
An analogy: You want to eat food that isn't covered in ants. Ergo, you stock food in your larder, in you home.
This doesn't mean you go out and crush every ant that can see your home, but if you find ants in the larder, you squish them without a single thought. If they come back, you spray and put out traps, etc. Again, if ants can find a way into your larder, they will; so the only way to keep your food safe is to keep your home impregnable to ants. This is not saying "I want a home impregnable to ants - I want food without ants, ergo, I must have a home impregnable to ants." Ants that get in are just an annoyance, not a failure.
If you beloved child "goes rogue" and starts trying to bring ants into your home, tries to make sure every ant in the world knows where your twinkies are kept; they're on track for a grounding (or worse) and move ants are going to die.
However, the underlying question remains: since there is no Sybaris or Lunacy involved with the cogs of the GM, how would it suppress attempts to expose it by Demons?
The answer is, "By whatever means necessary" - again, Nep's answer is spot on.
It appears this answer is unsatisfying because you envision some Demon's scheme that would expose the GM - ergo, the question could be refined to "How would the GM suppress a Demon trying to expose it via...?"
Unfortunately, that invokes only subjective answers, because the GM is under the ST's control. This StackExchange isn't a good place for mining answers to "How do I stop this plot I envisioned?" type of questions.
Here's an example: Demon Darren resolves to expose the GM, regardless of whether it costs his life or not; he goes to Central Park, in broad daylight, sheds his cover, and preaches the existence of the GM to everyone there.
There's at least one Angel, an observer type, that witness this from Twilight. How does the GM respond?
- One response might be to dispatch the moral police - "Psychotic cosplay enthusiast takes hostages downtown, shots fired" and, via corrupt cops in the system, order to shoot on sight. Either Darren gets killed, or, hopefully, is forced to kill some police in order to escape.
Then, control the narrative: every article about Darren and what he said gets flooded with comments - make it about police brutality, make it about mental healthcare. If he's dead, plant evidence, linking Darren to pedophilia and furries; spam videos with comments about CGI and crisis actors. If he's still out there, start a blog impersonating him revealing the "truth" about the moon being an optical illusion, that he's a reborn dragon, etc.
- Send out the assassins to cut him down. Cue the marketing: Make this avant-garde play go viral! Street performance! Awesome special effects!
If there's any collateral, edit their facebooks to mention about them being extras, paid for realism, and that they had to sign a NDC and disappear for a few months afterwards. Meanwhile, city government is furious this "performance" was put on without a permit, and the company claiming responsibility has to "put this project on hiatus while it is re-tooled. But stay invested - more crazy, heretical, wire-fighting action to come!" (Yes, this could involve a GM-influenced governing body appearing to go against a GM puppet company. Happens all the time.)
- Personally, my GM would just gas them. Keep some nerve agents in the warehouse that cause hallucinations, fever, seizures, and death. When the Central Park Angel reports this trouble, gas the whole lot with a generous margin of error. It's a terrible, horrible terrorist attack - that the nation can fortify itself against by ensuring electronic surveillance is even easier to obtain for faceless government agents (some of whom are Angels.)
Again, it's all down to the ST to step in and say, "What would I do to reduce or discredit this exposure?" bearing in mind the GM doesn't have a sense of morality that values human life.