I think you got part of that wrong.
Turkey did NOT help us in our invasion of Iraq.
Haven’t we been using them for a stageing base?
Turkey has been giving aid right along after the initial invasion, or rather, the Turkish army has, not with troops, but with provision of space, intelligence, etc. The Army is not quite the same thing as the Government. The only reason the Army has not removed this government is the desire to join Europe. It would better for everyone concerned if Europe would finally tell Turkey NO. Then the Army would do what the Army is constitutionally directed to do, protect The Turkish Republican state.