If you're already an expert at safely soldering and desoldering teeny tiny size-of-a-flea surface mount components, then yeah, it's trivial to remove.

But if you've never done that kind of thing before, no, it's completely nontrivial and you risk permanently damaging the display board.

The other issue is your stated desire to re-sell the illumination kit. After you remove the kit, the LEDs might not be easily installable into a new player, and the resistor pack might be completely blobbed up and nearly impossible to re-install.

Installing the LEDs depends on being able to stick all the way through the display board and then you can solder the long legs in place and clip off the excess. If you pull off the LEDs, then you might not be able to put them in a new player because you don't have the leg-length to put them through the new board. But... the LEDs are cheap and they aren't the tricky part of the kit anyway. You could buy a set of new LEDs for the new owner. The resistor pack is similar: You could just order a new one for the new owner.