If it's silk screened there's two issues that have to be addressed.
First, is there a layer of clear lacquer over the logo? If you have to scrape the clearcoat off, blending a new layer can be difficult. Even if you sand the entire surface matte the edge may end up visible at least at certain angles.
Second, has the white paint diluted the black and partially blended in? If so, you'd have to take quite a lot off which poses a risk of sanding through the paint.
It looks like the logo is just white paint silk screened over the glossy black. I'm sayin this because the "R" has worn out a bit. Try to feel if the letters are proud with your fingertips. You can try to scrape that "R" a bit more with a scalpel or razor blade - very carefully, you don't want to dig any grooves! Use the blade like a scraper, working your way from the outside in. If that works, continue with the entire area. Of you can try with the steel wool right away, although I suppose the bolder letters would be a pain to remove with that.
If you can scrape the text off, the next step would be to sand the area matte starting with some premium quality paper. 3M makes some very good papers that shouldn't clog or stick even when used dry. Wet-or-dry paper can also be used with a drop of soap added to the water. Start from about 600 grit to remove the scraping marks, working in one direction only. Continue with higher grits changing the sanding direction by 45 deg at every grit change. After 2000 you can move to a scratch removing compound and finally buff and wax.