Short version: The universe is a Symphony. Angels and demons aren't supposed to be on Earth. When they do miraculous things on Earth, it causes bad sounds (Disturbance) in the Symphony. Other Celestials can hear the Disturbance and are likely to show up and see who the new kid is.
Except that, except in extreme cases, the Disturbance isn't really that loud or likely to be heard, unless the other Celestial is right down the block at the 7-11. So it isn't much of a discouragement.
What if it stuck around? Had a half-life, like toxic waste, and polluted the Symphonic environment? A little bit here and there - eh, nobody's going to notice. But over time, if it gets pumped in faster than it decays, things get... off. The world doesn't work quite the way it should.
If you're the Dear Spouse, that could be an excuse for cryptozoology and other such fun. More seriously, you ever wonder why some sections of the planet - say the Balkans, or the Middle East - seem so perpetually screwed up all the time? Yup - Symphonic pollution. (Why the Balkans are polluted, I don't know, but the Middle East, site of Heaven's tinkering with monotheism, is perfectly explicable in In Nomine canon as a Disturbance dump. How many times did Gabriel manifest, in Celestial form, to Mohamed?)
And any Celestial attempts to fix the problem tend to make it worse; like tinkering with Fates and Destinies, Celestial interference in this process tends to screw it up. It has to die out on its own, or else the humans have to do... something... to repair the Symphony.
It still may not be much of a discouragement - the PCs are likely just peeing in the ocean, metaphorically speaking - but it gives their Superiors more of a reason to come down hard on them for excessive Disturbance.