I’ve dealt with this on a small city patio, and the trick is to make your furniture less interesting, less accessible, and less tasty to squirrels. Squirrels usually chew because they’re maintaining their teeth, exploring, or following food smells. So start by removing the attractants. Sweep crumbs off tables and chairs, wipe down surfaces with mild soap and water, and bring cushions, seat pads, and any fabric covers indoors when you’re not using them. Don’t leave birdseed, pet food, trash, or fallen fruit nearby, since those smells can turn your patio into a squirrel buffet.
Next, make the furniture harder to chew. Wrap exposed wooden legs or arms with metal flashing or hardware cloth, or fit smooth metal caps over the corners squirrels like to gnaw. I’ve also had decent luck using a commercial squirrel repellent that contains capsaicin or pepper wax, but test it on a hidden spot first and reapply after rain. Avoid mothballs and anything that could harm pets, kids, or wildlife. A motion-activated sprinkler can help in a yard or larger patio, though it’s less practical on a tiny balcony.
If squirrels are determined, give them a barrier rather than a snack. Store furniture under a heavy-duty cover when possible, keep it away from railings and overhanging branches, and secure trash cans. For chew marks that already exist, sand the rough edges, fill deeper gouges with wood filler, and seal the surface so moisture doesn’t get in. I’d skip poison and glue traps entirely, especially in an urban area. A mix of cleaning, physical barriers, and a little repellent usually gets the message across without turning your outdoor space into a battle zone.