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Sorry to disappoint, but exploding something at GEO would make things worse.
All satellites in orbit of Earth will experience atmospheric drag. Even the Moon is bumping into gas atoms.
Geostationary satellites will eventually fall. It might take millions of years, but eventually the thin atmosphere will slow those satellites down enough that their orbit will fall into the thick, lower atmosphere where they'll burn up or crash into the Earth's surface.
Exploding a satellite up there will just make a shotgun spray of projectiles that will still take millions of years to fall. Assuming the projectiles shoot off in all directions fairly evenly, then the ones that get shot backwards relative to the motion of the satellite will end up in a lower orbit that will decay faster. The pieces that get shot forward might actually escape Earth orbit all together and become little asteroids orbiting the Sun.
The thing that's special about geostationary orbit isn't that the orbit of things at that altitude does not decay. That altitude is special because at that altitude, orbital speed is equal to the Earth's rotational speed. A satellite at that altitude over the equator will remain over that same longitude - it won't rise and set like the Moon, it will remain in the same spot overhead both night and day.
Hmm, it looks like you need a bit over a kilometer per second to escape Earth from GEO. I guess that's not impossible with high explosives. I don't think any shrapnel would make it back to earth, though, since they'd have to lose most of the 3 km/s
Losing ~1.4 km/s at GEO would put a fragment into geostationary transfer orbit, with one side of the elliptical orbit at geostationary altitude and the other side at low orbit altitude where it would experience increased drag.
Ah, okay. So not quite most then. My bad; orbital mechanics takes some getting used to even at this elementary level.
Also, I just noticed, relevant username.