My initial thought is the curved area isn't damaged at all. It is part of the flap, and when extended, if I am correct, comes close enough in proximity to the main landing gear to necessitate the cutout design, lest the wheel come in contact with it and grind it into that shape anyway.
I have been an aircraft mechanic all my life. I have an A&P license and I have worked on every kind of aircraft you can think of, from a Piper Cub to high performance jet fighters in the military to jumbo jets, 747's and stuff like that. Am I bragging? No, no,no. What I am trying to say is that you made one hell of good call on this thing. You looked at it and came to a conclusion that could be 100% correct. I don't know what your background is but the average person would not have any idea what they were looking at and would not even be able to make a guess about what it is. I have to commend you, very good.
However, after heaping praise on you and patting you on the back over the last few minutes I have to tell you that I have my own opinion about what we are looking at, and because of my experience and ginormous ego I think my opinion is correct. I am hoping that later on we will get more information on this story to determine who is correct.
It's hard to tell a whole lot from the photo but I have to agree with you, I think it's a flap. It isn't far enough out on the wing to be an aileron, it's not in the right location to be a spoiler. The way it appears to be attached to the fairing sticking out the back of the wing would make it a pretty standard configuration. However I don't think it is far enough inboard for there to be a clearance problem between it and the landing gear. If you are able to crawl around under big jets you will notice that the designers put as much distance between the landing gear/wheels and the flaps as possible. The landing gear also tends to be mounted inboard so it doesn't sit directly in front of the flaps. The reasons should be obvious. You don't want anything thrown up by the wheels, ice, snow, water? to be thrown into the flaps. This causes a tremendous amount of damage to the aircraft.
Lastly, I have never in all the years I have spent working on aircraft seen a cutout like this on a flap for the purpose of clearance. Not on any commercial aircraft or any other aircraft I can think of. So after reading the OP and looking at the picture and knowing what I know I think this is temporary repair. The flap had some type of damage or was cracked or whatever. The maintenance crew came out and cut out the damaged area, smoothed and blended all the edges, sealed up any openings and that's it, back in business. Temporary repairs are accepted by every part of the aviation industry and have been around since the Wright brothers first flight. They are authorized by the aircraft manufacturer and the FAA. Virtually every maintenance manual or structural repair manual has instructions for doing temporary repairs. I have done dozens of them myself. They don't affect aircraft performance or safety in any way.
Anybody out there who has read this and would like to offer their observations, comments, views, opinions or just hurl general insults at me, have at it.
FINAL NOTE: I refuse to entertain any theories that have to do with chem trails or alien abduction.
