Why did Luke Skywalker throw his lightsaber

Why and how were Luke Skywalker's hands freed before going into the Carkoon Pit on the Dune Sea in ROTJ?

As I can best judge, the loss of the handcuffs actually happens earlier, during the speech in which Jabba offers to make her beg for her life, as shown in this picture:

Luke's arms couldn't be that far apart and his hands were still cuffed. Before that, it is slightly ambiguous whether the cuffs are still on. Luke keeps his wrists crossed as he rushes to the plank.

I can't find any evidence that the cuffs were removed, but there was enough time while Jabba was speaking for it to happen. Why they might have removed the cuffs, maybe they are just too frugal, don't want to lose the cuffs to the Sarlacc pit and think that people are helpless without their weapons. Still, you'd think that at least they wouldn't unlock the Wookiee.

One version of the script includes the following:

25 EXT SARLACC PIT 25

The convoy drives over a huge sand pit. The Sail Barge stops on one side of the sink, as does the Escort Skiff. But the prisoner's boat moves right over the center and floats. At the bottom of the deep sand cone is a repulsive, slimy hole surrounded by thousands of needle-sharp teeth. This is the SARLACC. A plank extends from the edge of the prisoner's boat. The guards release Luke's chains and push him onto the plank over the Sarlacc's mouth.

In any case, it is pretty clear that anyone would have seen that they were no longer tied up and that no one was responding anymore. So it is either a continuity error or an intent of Jabba's thugs.

JMFB

+1 correct answer. Since you theorized that it should be "thrifty" before the other answer, and you posted the script before the other answer, too, I'll give you the correct answer. Well done.

FuzzyBoots

Plus the hand-drawn circle. :-P

FuzzyBoots

Unyielding

I corrected the spelling of "Wookiee". They wrote it "Wookie". The smart quotes are just a bonus from some browser extensions.