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Why the hell was Grievious COUGHING?!
I think that was a reference to Mace Windu's force choke at the end of the Clone Wars cartoon series. Mace squished Grievous' innards using the force. I noticed tons of little nods to the Clone Wars cartoons.
No explanation makes it any better, though. The coughing was stupid and distracting in Revenge of the Sith.