Sadly its a scourge of modern locking wheel nuts and Jag/Land Rover seem worse than most. It certainly isn't the locking tool on there and id say whats left over is probably an attempt to remove previously. There isn’t an easy answer to this, with a recess like that you’ll always do some kind of damage one way or another.
One thing that you can try is to remove all the other nuts so that its hanging on the one buggered one and pull the wheel towards you so youre essentially loading the nut, this may be enough to give it a small amount of movement, with care you may be able to chisel the nut around enough to get it moving. Don’t think you've got a lot of room there but an Irwin may fit, if not there is always an option to weld a larger nut on there which would also cause a little heat and help removal. Either way its not going to be easy unless you get lucky.
Edit….if only people would remove the locking nut with a bar instead of using impact guns this issue would be greatly reduced