Must...Obey...Gremlin!

[Encaitare]

Were the soldiers of the King really mindless drones staggering around Meduseld chanting "Must...Obey...Gremlin?

Well, that's what I do... sneaky little worm...

I know this is a movie-discussion, but I can't help but bring up that line in the book where one of the Rohirrim says that if Wormtongue were there, he would know what to do. This implies that despite his obvious inclination to evil and lack of hygiene, he was at a time, a good councilor, and was always a very firm and decisive one. I agree that he probably did have "thugs" in the court who he swayed to his will, although I doubt they were sent by Saruman himself.

As for the original question, why the guards punched Eomer, perhaps Grima fed them lies about him, making him out to be a traitor, or something of that ilk. We do know that he has a tricksy way with words...