It's just a little surface rust so it's essentially a cosmetic problem at the moment. Assuming you want to keep the hitch on the bike all the time (that is after all the point of it) then I suggest that after removing any loose material you wipe grease over it to provide a barrier against moisture. You wouldn't have to do it after every use but whenever you clean the bike/oil the chain. This will also deal with the way the rust makes it harder to fit the trailer to the hitch. It also darkens the remaining rust temporarily, making it less obvious.
Mine is a different design (with a pin going through it) but I assume that yours also doesn't rely on friction (which wouldn't be safe). In fact yours may even move slightly around the hitch, which would abrade the paint.