Just wait until you put it in for a service and get it done then. I think it will probably pick up a few more scratches by then anyway. When it comes back from the service it will look like new.
I recommend the "avert you gaze" strategy. Don't look at it. Eventually it will have brothers and sisters to keep in company.
If you fuss over every little mark, you'll eventually make a mess of the case trying to keep it pristine.
...or just get a cape cod cloth and it will probably come right off (if not too deep - hard to tell from the photo). Just remember to tape off the brushed parts so you don't accidentally polish them too.
Keep wearing it and put more marks on it. Or if you dont want marks, put it in a box and leave in the drawer somewhere never to see light of day, and buy a cheap watch that you dont care if you scratch or not. In my mind watches are made to be worn and used, and part of that is putting scratches on it. Wear it with pride, enjoy it and dont worry about scratches.
I bet this guy wouldn't give a damn about scratches and marks on a watch. (no offence intended) Steve McQueen. (in case someone was wondering)
If they can't read it on his jacket, I don't think they'd be able to read your post. [emoji23][emoji23][emoji23] Somehow I don't think this guy cared about scratches on his watch either (Cousteau wearing the Marine Chronometer): Sent from my iPhone using Tapatalk
Initially its a eye sore. But after a while, you will get used to it. Let it be and clear all it off when the watch is due for servicing.
Part and parcel of wearing a watch. Just like driving a new car, before long there will likely be scratches, bumps, etc... Just enjoy the watch [emoji3] Sent from my iPhone using Tapatalk
Although I agree with the majority of the people (it's going to happen) it doesn't take the sting out of the first scratch. Sent from my iPhone using Tapatalk