@Ari49608 In Maui, we actually have this exact issue. Excellent cleaner, vacuums and then mops all the floors. A few years back, a guest complained her socks were dirty.
We live in a beach environment, and all kinds of particles float up from the beach, not to mention the mud and sand that the guests themselves bring in. Your guest might be sliding around in the dirt from their shoes. How long after check-in was the pic taken?
Also, we had our popcorn ceilings removed and the ceiling redrywalled in 2018. Ever since then, our coffee table gets a sprinkling of small white particles every few days. There is a unit above us. Either those particles are coming up from the beach, or perhaps movement upstairs disturbs the new ceiling. Who knows?
I’m starting to wonder if this kind of thing might not be uncommon in certain locations. I’m a little leery of your particular guest, though. See the other dirty sock(s) on the floor in the pic? It’s as if they had a party taking socks in their hands and wiping them around the room. Unless this is something like a fabrication lab where they are making microchips and you have to wear a spacesuit to enter, you are bound to pick something up if you wipe your white sock all around the room. This reminds me of guests that move out stoves and refrigerators in the hopes that they can find proof that might warrant a refund.
In any event, you might be comforted to know that I’ve never had any other sock whistleblowers contacting me since that fateful day in 2019. This guest did not ask for a refund, by the way.
Now that I’m through expressing my cynicism, and to answer your question, in all honesty I would 1) offer to reclean the floors, and if they don’t want that, 2) offer a gift certificate or to pay for a dinner for the guest. It’s usually a good idea to try to appease a guest, no matter how absurd the situation. No cash refunds, though.