Possible Clues:

• Chaotic study in need of a clean?
• Sooty perhaps having obligation to hold Sweep but not cry
• Dirty and powdery
• Like the top of most refrigerators
• Like some top-shelf products?
• Clearly little-used
• Failing the white glove test
• Needing cleaning with a cloth, in a way
• Failing the white-glove test, say
• Needing cleaning