how can I clean a prefinished door?
I would try, in order of escalating cleaning function, these series of things until a suitable result has been obtained:


Wiping with a clean dry cloth.
Apply a little (15 ml/1 Tbsp) white vinegar to a paper towel and wipe.  Rinse with a wet (water) paper towel.
Combined with vinegar or dish detergent (for hand washing), use a rough cloth or mild scrub brush (pink or white Scotch brite).
Green Scotch bright and soap.  Repainting might be necessary afterward.
220 grit sandpaper
150 grit sandpaper
100 grit sandpaper
woodworking plane
replace the door