The Iraqi CAA may not have the ability or capacity to do so, YET. How would you re-cert with no FAA check airmen in the country?
Reciprocal means "two ways". That means the FAA has to accept the Iraq licence if the Iraqis are to accept the FAA's licence. No?
Is that the case at present? I don't know. But from your post, I'd have to conclude there is no reciprocal agreement.
check it out.
Willie