I have similar smaller in length key marks from people who did it to the previous owner of my car. If you have a buffer or you just wax the s**t out of it, it will make it much less visible. This won't completely fix it though.
I don't recommend you go through insurance. That will be way too costly. Also don't get a completely new paintjob. This doesn't seem that deep...
So either buff it yourself or get a professional buffer to try and get it out. If that doesn't work, then go the touch up paint route. I warn you though, 99% of touch up paints are S**T and will not match your car. I learned the hard way from trying to touch up my front bumper, and it ended up looking worse than before, so I just got the whole thing re-painted ($400). Goodluck!