Firstly, this thread should probably be moved to SF/F.
Secondly, the "mark" that Jack left on Beckett was never made clear, not even in At World's End. Supposedly, the writers came up with some backstory about how that occurred. 13 years ago, Beckett hired Jack to transport some cargo. Jack agreed until he learned that the cargo was slaves. He freed the slaves, so Beckett had his ship, the Wicked Wench, burned and sunk. This was where Davy Jones came into the picture. He raised the ship from the depths for Jack. Jack, seeing that the fire had scorched the wood black, rechristened the ship the Black Pearl.
I find that a weak explanation. Beckett holds a deep grudge against Jack because Jack cheated him on a business deal?
I prefer my friend's theory. You know how Jack is always going on about eunuchs?...