What to use to clean headliner
I would use some Woolite carpet cleaner and spray it on a sponge and carefully work it in the stains, let it dry and vacuum off, don't get in a hurry or too wet, you can rub the covering right off it is not very substantial material.
TOUGH STUFF spray on, let it sit a little, then wipe it clean with a clean colorfast DAMP cloth.
I would ask for advice at the Lincoln dealership. They know lots of little cleaning tips. If you use the wrong stuff you risk ruining the headliner and that would be very expensive to replace.
Looking for a Used MKZ in your area?
CarGurus has 15,206 nationwide MKZ listings starting at $2,995.
Search Lincoln MKZ Questions
Lincoln MKZ Experts