To address the issue, simply fill the scratch with the Sharpie until it's entirely covered in permanent ink. Once dry, gently remove any excess ink with the alcohol prep pad.
While there was some debate in the comments about the effectiveness of this hack, its low cost makes it worth considering. However, the method is most suitable for minor scratches.
If you're concerned about using a black Sharpie on lighter floors, there are wood markers available that match various floor shades, such as the RamPro Furniture Markers Touch up.
These markers can be used much like the Sharpie, but there is no need for the alcohol prep pad afterward. Just let them dry, and your floors will look as