On a steel bike it is important to fill in the deep scratches to prevent rust. If you can see bare metal, it's a good idea to touch it up. If you have rubbing alcohol, prep with that, then paint (testors enamel is good).

If it already shows corrosion, you can sand it off a bit with a really light grit sand paper. If you want to get really fancy, you can use a metal primer before you paint.