However, it's important to note that the real mark Jack left on Beckett was not physical, but rather psychological. The encounter left Beckett obsessed with finding and killing Jack, making him a relentless and even more dangerous adversary. Jack's rebellious spirit and ability to escape Beckett's clutches ultimately contributed to Beckett's downfall.
So, while the sword cut is a visible mark, the true mark Jack left on Beckett was the fuel he added to Beckett's obsession and ultimately his demise.