DIAGNOSIS You're right to be careful—the grille is not removable for washing, and liquids are the enemy. Dust and light smudges are the main things you'll deal with.
FIX For routine dust, use a soft, dry microfiber cloth. Gently wipe in one direction along the fabric weave. For a bit more cleaning power, you can very slightly dampen a corner of the cloth with *only* water—just a few drops—and wring it out completely so it's barely damp. Wipe gently again, and immediately follow with a dry part of the cloth. Never spray any liquid directly onto the grille.
IF THAT DIDN'T WORK For more stubborn spots, Sonos suggests using a soft-bristled brush, like a clean, dry paintbrush or a soft-bristled toothbrush reserved for cleaning. Brush gently in one direction to lift dust and debris from the fabric without pushing it in deeper.
HEADS UP Never use vacuum cleaner attachments, paper towels (they can snag), or any cleaning chemicals like glass cleaner, soap, or alcohol. These can stain the fabric, break down the adhesive holding it on, or damage the speakers behind it. The goal is light, dry maintenance.