What wasps are actually doing when they 'chew' wood
Social wasps — paper wasps, yellowjackets, and hornets — build their nests out of a material that looks and behaves almost exactly like paper, because that's essentially what it is. A foraging worker lands on a weathered board, a dead branch, or an unpainted fence rail, grips the wood with her mandibles, and scrapes off a small quantity of loose surface fiber. Back at the nest, she mixes those fibers with saliva into a pulp, spreads it in thin layers, and lets it dry into the gray or brown papery material that makes up the nest envelope and the honeycomb-like comb inside it.
A peer-reviewed study of nest-material foraging describes exactly what wasps target: 'sound or weathered wood from fences, posts, dead trees, decayed wood, bark of living trees and shrubs.' Notice what's on that list — weathered, decayed, dead. Wasps are drawn to wood that's already partway broken down by sun and moisture, because it's easier to scrape loose fiber from it. That's also why the marks show up disproportionately on old fences and unfinished sheds rather than new decking.

