I was thinking some transparent filler maybe, and grinding/polishing it down? There’s some varnish on the wood anyway.
Look for other advice for repairing them, but making your couch feet bigger and softer with tennis balls or felt should prevent it from worsening.
Make the dents everywhere, and no one will know
You’re screwed, dude. That’s nothing you can easily fix. Most tips in this threat require you to do the whole room, as just fixing this one spot will most likely be pretty obvious.
Next time, try to use something broader and softer than a sheet of paper to dampen your couch’s feet - especially on wooden floor.
There’s the “right” way and then there’s what’s practical. Here’s the “right” way:
Rough sand the entire floor to wood. Fill the voids with Starbond CA glue of the appropriate color, low viscosity for leveling. Fine sand the entire floor. Refinish with oil-based polyurathane.
If you know what you’re doing then this will take three days, most of it dry time. If you don’t know what you’re doing then one way or another you’ll destroy the floor during rough sanding.
Cover it with a rug
I’m not an expert but:
Resurfacing might fix this if it is solid hardwood, since you are essentially sanding down a layer and refinishing the new top layer. The dents look kind of deep, though, and may require extra sanding to take the wood down far enough.
Not a professional but they look kind of deep and big might need to be replaced or covered with a rug (we won’t tell anyone they’re there)
Steam might be able to fix those. But I don’t know if that would work with varnish on the wood.
I tried letting some water sit for some hours in one dent, to see if the wood would expand - but nothing happened. I guess that would rule out steam, unless I remove the varnish in the dents first?
You have to remove the varnish by sanding first, then try to iron the floor. There may be poor contact in the middle so try ironing the other edges.
Other than that, you are gonna have to get new boards installed.
Yeah, OP wants to work over a large are, not just where the dents are.
