I did a lot of freeze frames in that movie and tried to understand how it was done and I concluded its a movie prop. There's at least two shemaghs involved if they're normal sized shamaghs (maybe they gave Mr.Fiennes a table cloth, I don't know). You'll also notice the bullshit when he seemingly "unclips" the portion over his nose to reveal his face.
Here's the movie clip for those who have no idea wtf we're talking about
YouTube- The Hurt Locker -Contractors- British and South Afrikan