I use 0000 steel wool. Nothing will take deep scrapes and bruises out except a full re-surfacing and then rechroming.

I use Turtle wax Rubbing compound and a soft solid cloth. Something like a thick, tightly woven sock and lots of pressure and patience. It will take some of them out without taking the shine off the chrome. Steel wool kills the sheen. When you use rubbing compound, it takes longer, but it polishes the chrome, not dulling it. It is a micro abrassive and that is what takes oxidation and surface scratches out of paint and brings back the shine. As O-D states, deeper scratches don't go away, but they can be diminished with a good polishing compound and maybe even a small buffing wheel on your Dremel tool with the compound will make quicker work of the chrome, kind of like my use of the detailing brush, except it is more serious for this type of work. The detailing brush is great for the general cleaning and polishing. For the tedious and finer work are attempting, a buffer wheel and compound on the Dremel is the prescribed method I use.