From this link, (specifically in number 8)
8. NO ONE TAKES GANDALF’S ‘WALKING STICK’
One of the subplots in Two Towers is Théoden’s possession by Saruman with the help of Gríma Wormtongue. Aragorn, Legolas and Gimli along with Gandalf the White, head on to Rohan to exorcise Théoden. Before they are allowed to go in, the men demand they remove all their weapons, including Gandalf’s staff. Somehow Gandalf convinces them he is a helpless old man with a walking stick and they believe him.
We later found out Gríma specifically told them to take his staff. Are they fools? Can Gandalf Jedi mind trick people as well?
The worst part isn’t that Gandalf tricks these men to think his staff is just a walking stick. The worst part is when he walks in with his staff exposed, but it is a surprise to everyone when he reveals it to Gríma. It is a blinding white staff. How did no one see it?
So it makes sense to me that the henchmen are fools because they were ordered by Grima Wormtongue to get his staff.