Any idea what product I can use to fix this? (with pic)

[SlightlyJaded]

Oak floor with a lightened 'wash/finish'

We have bar stools around the kitchen island and the felt feet have come off (and we were crap at replacing them) and now the floor is scratched 'beyond' the light top coat. So it always looks dirty.

Any idea of a suitable product to touch it up? I don't care if it's not perfect but it looks shit. Floor is only three years old but floor people (Flooring Direct) have been worse than useless.

I would probably make up a wash of emulsion , white first then possibly very light grey once it has dried if necessary. Make it quite stiff and rub it in rather than brush on. If the scratches are really deep, you might need two or three coats.Matt varnish over the top will seal it.

Then get some felt pads with nails. And put them in the bottom of the stools.

just seen you have metal stool,feet😳 stick some felt pads on with no more nails.

I would probably just cover it up with something and staple that in place to stop it moving.

The damage looks quite deep, but I would still try sanding and re-sealing if you can find a suitable stain / sealer. Test on an off cut if you have some..

First post offers the best solution. Use some watered down basic white paint and try a thin coat. Wait till dry. Inspect for colour results , adjust the colour and reapply. It would probably look better if you tried using coats of different colors than trying to get it to be the exact colour. Use a small brush, apply unevenly. You can always resand areas you don't like. Go slowly. Good luck.

For the diluted paint suggestions - do you mean emulsion?

Yes. A water based paint. Be sure your floor is clean. Wipe it down with a bit of white spirit. Once you are satisfied with the results, (don't seek perfection) give it a coat of matte acrylic varnish to seal it. If you continue to put the chairs in the same spot it won't last long...
Maybe seek another type of flooring ?