It looks the like the real reason for the existence of the Zaytun unit is having some issues:

The Iraqi government has suspended crude oil exports to Korea’s SK Energy, following a call on Korean businesses to halt development of oil fields controlled by the Kurdistan Regional Government.

SK Energy on Tuesday said the Iraqi government in late December last year threatened to suspend crude oil exports unless a Korean consortium including SK stops oil exploration in Kurdistan. It suspended the exports on Jan. 1.

Iraqi authorities maintain that it was illegal for the Korean companies to sign oil-related contracts with the semi-autonomous Kurdistan Regional Government in northern Iraq without approval from central government. The Iraqi central government found fault with a contract for the drilling rights in the Bazian oil field in the northern Iraqi region of Dahuk, which was signed between the consortium, which also includes Korea National Oil Corp (KNOC), and the Kurdistan Regional Government in mid-November last year. [Chosun Ilbo]

This looks like something a few bribes to central Iraqi government should easily be able to take care of.