Lots of good comments on this.
What do your requirements say? If cleanliness is one of the requirements, then clearly the supplier still has responsibility after the inspection is done: right up to the point of leaving on the truck.
If it turns out that the source inspector should also do a product inspection, so be it: open a box just before shipment, look at a sample and check for cleanliness that meets your requirement. At this point the inspector can note the traceability and see how long the parts were staged where. The inspector can look around for how debris would land on the parts. Would they be staged near a vent, or next to a machine, etc. Can the inspector take pictures on hos phone and send them to you? Or maybe the supplier would prefer an audit. I am thinking not.
So the QM says he personally cleans and packs these? That seems to me like work for someone besides the QM. Or maybe he doesn't do this for every single lot.
I agree with
@Golfman25: start with pictures, compare them to requirements, and ask for the supplier to partner with you to solve this problem so everyone can get back to what they'd prefer doing: counting money.