For Expert Delivery, only colored gear (gear which has its name and icon display as a certain color - green, blue, pink) is of interest to the QM. And even then, some colored gear is unable to be turned into the QM.

Beyond that, I have heard that what you can turn in via Expert Delivery is also dependent on your current rank within the GC. If this is true, as you achieve higher GC ranks, you should find more and more items available to be turned in.