Oldest Snake
Member
Maybe the NK's 'mark' isn't a mark in the sense that Bran has been 'branded' by him, it's just the consequence of him making physical contact with Bran (a freezer burn!). The mark itself might not be important, he just needs to touch someone whilst they're greenseeing, he didn't use an existing 'mark' on Bran to enter the cave after all, he simply touched him in a vision when Bran was physically inside of the cave.
He could do the same thing again, touch Bran whilst he's greenseeing, after he has passed the wall and use that connection to breach The Wall's magic the same way he did at the cave.
He could do the same thing again, touch Bran whilst he's greenseeing, after he has passed the wall and use that connection to breach The Wall's magic the same way he did at the cave.