Notice that the scratch is WHITE. Why is the scratch white?
Because the surface of the scratch is rough. Rough surfaces scatter light by reflecting and refracting it in different directions, and, just like a prism, each facet on a rough surface will refract each different frequency of light in a slightly different direction. That light then gets reflected off the surface of the wood, or something in the wood and reflects back in different directions. The result is that your eye sees different frequencies of light coming from different spots on the surface of the scratch all at the same time.
So, your scratch is white for exactly the same reason that a clowd, or a snowbank or the head my beer are all white, even though nothing inside any of these things is white in colour. It's the combination of different colours of light coming from millions of places in the clowd or on the surface of the scratch all at the same that makes it look "white".
What you need to do is get a small artist's paint brush and paint over that scratch with clear nail polish (which is basically clear acrylic paint).
That will coat the surface of the scratch and change it into tiny gulley with a smooth surface, thereby eliminating most of the scattering of light. And, that in turn will eliminate most of the white colour you're seeing. Once you do that, you will still see "something" there because the non-flat surface of that miniature gully will cause an aberation in the way light is reflected off the surface of the floor. However, that "something" should be much less visible (and noticable) than the white scratch you have now.
If you can tell me whether the scratch is in a synthetic coating over plastic laminate, or in a water based or oil based coating over real wood, it's very possible that we can find a clear liquid you can paint onto that scratch that would stick to it and be more compatable with the finish than clear acrylic nail polish.
You should also be aware that by painting over that scratch with a clear fluid that dries hard (like clear nail polish) until you end up with a "bump" along the scratch line, and then scraping down the surface to make it flat, and then applying a thin coat of any clear finish over the scraped area (to make it smooth), you should be able to hide that scratch almost completely.
Or, at least, that's what you should be able to do according to Fresnell's Law of Reflection, which when you're looking at the scratch at a 90 degree angle (like the camera shot was taken) breaks down to...
Fraction of reflected light = ((R1-R2)/(R1+R2)**2
...where R1 and R2 are the refractive indices on each side of a reflecting interface.
Fresnel equations - Wikipedia, the free encyclopedia
So, what you have now is air (with a refractive index of 1.0) on top of a clear waterbased polyurethane (presumably) with a refractive index of 1.4 (guessing).
That means that the percentage of light reflected off of the clear finish is:
R = (0.4/2.4) squared, or 0.027777 or about 2.8 percent
or, 2.8 percent of the incident light is reflected off the clear finish over the wood, and the remaining 97 percent of the light goes into that clear finish and reflects or is absorbed by the underlying wood.
If you now fill that scratch with clear nail polish remover, which, being a solid, has a higher refractive index much closer to that of clear water based polyurethane, say 1.5, then the amunt of light reflected off the surface of the clear nail polish becomes:
R = ((1.5 - 1.0)/(1.5 + 1.0)**2 = (0.5/2.5)**2 = 0.04 = 4 percent
Whereas the amount of light reflected off the nail polish/waterbased poly interface becomes:
R = ((1.5 - 1.4)/(1.5 + 1.4))**2 = (0.1/2.9)**2 = 0.00119 or 1/8th of 1 percent
Thus, by filling in the scratch with a clear solid material, then you eliminate the white discolouration, and you have almost exactly the same amount of light reflecting off the smooth flat surface, so that you couldn't percieve any scratch. Any roughness at the nail polish/waterbased poly interface would be imperceptable because only a very tiny amount of light would be reflected at that interface (1/8 of 1 percent) of the incident light. So, it wouldn't matter if that interface was smooth or jagged because it would be invisible anyway because of the tiny amount of light reflected from that interface.
Ideally, it would be best to fill in the scratch with the same finish that is on the floor now. That way the refractive index of the "clear nail polish" and the "water based poly" would be the same, and the numerator in Fresnel's equation will always be 0, meaning NO light is reflected from the clear nail polish/water based poly interface, making it totally invisible.