To me, this is not a worn rope. This is a fairly new rope that had an encounter with a handsaw, pole saw, chainsaw, etc. Hopefully, you know the history of the nick and can remedy. Your question is really, how serious, right? Know your line. Cougar is 24 strand double braid, load is shared between core and cover. The damage appears to be only to the cover. You have twenty four separate strands comprising the braided cover. It appears from your photo one red strand is fully severed, one yellow strand has been picked, and maybe a black strand too, I can't tell from here. If that's true, 23/24 strands are intact on your cover. Presumably the core is fully intact. This damage doesn't hit "cut me now so no one ever climbs on me again" threshold. However, that spot should be monitored. It's easily monitored by feel; every time you pull that line out, put it away, or run a hitch or mechanical over it, you'll get a feel. Then visually inspect. If you know the history of your line, and you know the reason it all works, you'll be able to answer this question for every different type of line you employ.
Make a clean cut with a sharp scissors. Burning the fray will leave a hard spot, for me this is worse than the nicked strand.
I believe the generally accepted guideline (I'm sure I'll be corrected if wrong!) is retire or cut a db 24 strand if four strands in a row are all completely severed. Four strands spread out is not an issue.
