Diagnosis
Right to be careful. That big lens has a special anti-reflective coating that's softer than glass. Standard cleaners and rough cloths will ruin it.
How to Fix It
Use only the proper tools. 1) Get a rocket air blower (like for camera lenses) to gently dislodge any loose dust. 2) For fingerprints or smudges, use a dry, ultra-soft microfiber cloth designed for eyeglasses or camera lenses. 3) Gently wipe in a circular motion from the center outward with almost no pressure. If it's stubborn, you can breathe lightly on the lens to fog it and use the dry cloth immediately.
If That Didn't Work
If a dry cloth won't remove a sticky residue, dampen a corner of the microfiber cloth with only distilled water—never tap water or spray. Wring it out completely so it's barely damp. Wipe gently, then immediately buff dry with the clean, dry side of the cloth.
Heads Up
Never use window cleaner, alcohol, ammonia-based solutions, or compressed air in a can (which can spit propellant). Don't rub in a back-and-forth motion, as that can grind particles into the coating. And always put the lens cover back on when not in use.