WOW! Looks like the Marrette® has melted! Well, I am sure it is NOT an original one, as I have seen them baked and brittle, never melted, so I guess that it is a cheap knock-off.
It appears they used a wire nut and it overheated and this is the feed for the GFI circuit?
Just cut off the bad wire, you may have to stretch the one from the outside, there is usually more length behind the box and then utilize a good quality wire nut, not the Dollar Store brand.
Also, looking at your picture, if you can stretch it enough, maybe eliminate the pigtail altogether and run the wire straight into the breaker.