I would imagine Iraq has a high percentage of unemployed, so no need to import labor.
Iraq is a very strict muslim country. Not many women work at all. It's likely impossible to find a local woman who would work as a live in domestic helper, so probably many filipino domestic helpers.
Educated filipinos are also working skilled jobs all over the world. They are in high demand for their combination of good english skills, decent education, and low wages they will accept. Many work in hotels, airports, hospitals, schools....
The fact that the Philippines bothers to have an embassy there is a good clue that there are a significant number of filipino workers.