Bicast - used couch purchase has strange melted looking damage around head area

[bbb]

I just bought this couch from craigslist and didn't see it had these markings on it. I would be very happy with the couch and price i paid if i can fix them. they look like the leather is almost dripping down on itself. i'm not sure how the markings came to be but here are some pictures:





here's the back side of the leather:



there is also this part, but it just needs some oil right?





anyways if someone knows how this damage came to be and especially how to fix it I would be so grateful.
thank you
b