The 'scratch' is in the FINISH. All vinyl floors have a finish on them 20mil, or 12mil or 30mil of polyurethane or even urethane. The scratch has caused the finish to separate from the layer of vinyl it is sitting on. That's why you cannot feel it...but it is there nonetheless.

There is no way to make something re-adhere to the material below. This type of scratch is part and parcel of flooring that is something other than porcelain tile. I'm sorry but the solution is either remove/replace the panel or live with it.

You are welcome to use permanent markers (felt pens...artist's style to get all the colours you want) and touch up the finish. The colour repair will probably last several years (it will eventually wear away with each mopping). By that time the floor will have aged-in and have a consistent look with minor scratches over the surface. These minor scratches are also part of what makes a floor look 'real'.

Of course the easiest thing to do is live with it for 6 weeks. If you are still 'seeing' the scratch after that length of time, then go ahead and fix it. I would start with the felt pens...and then move up the $$ ladder from there.