DIAGNOSIS: The screen is a standard capacitive touchscreen with a smudge-prone glass surface. Using the wrong cleaner can damage the oleophobic coating or seep inside.
FIX: Power off the thermostat at your furnace breaker for safety. Use a dry, soft, lint-free microfiber cloth (like for glasses) first. For stubborn smudges, lightly dampen a corner of the cloth with only water—distilled is best. Wipe gently, then immediately dry with the dry part of the cloth.
IF THAT DIDN'T WORK: For sticky residue, use a tiny amount of isopropyl alcohol (70% or less) on the cloth, not directly on the screen. Avoid the edges where the glass meets the plastic bezel to prevent liquid ingress.
HEADS UP: Never use window cleaners, kitchen sprays, solvents, or anything containing ammonia or abrasives. These will permanently haze or strip the screen coating. Don't spray anything directly onto the thermostat.