This probably won't be much help, but when I was working as a sales manager for Sandals Resorts I had to travel through out the Caribbean to the different islands for several days each month. Most of the USA sales managers went to the mall on one of the islands and went to a cell phone kiosk and were able to pick up really cheap cell phones that worked internationally (they used them to call home to the USA). There was no service plan or anything, you just bought international minutes (surprisingly cheap) that would be put on the phone. "Pay as you go".
There is a huge problem internationally in regards to fraud and long distance billing and calling cards were difficult to use (needed a pay phone) and no one wanted to risk adding an international plan to their regular cell phone that they used back here at home because of the possibility of all sorts of things getting billed on their bill. Not just calls they didn't make, there was problems with actual merchandise and 900 numbers getting added on to their bills without their authorization. Other countries don't monitor and control that sort of thing as well as the USA and dealing with overseas companies and trying to get unauthorized stuff off your bill was almost impossible. The "pay as you go" phones are much safer and more fraud proof.
That isn't much help in Iraq unless they can get to a nearby city that offers something similar.
It would be easier though for them to do it this way than figuring out how to buy the right phone/plan here and sending it over to them. I figured I'd share my experience just in case.
Do any of the military websites or forums have any info on this? You might want to give that a shot, I am sure it is a popular topic.