Rancor Pit Grate
About this scene:
Luke has fallen through a trapdoor in Jabba's palace, and is now in grave danger inside the Rancor pit. The monstrous Rancor is about to attempt to have him for dinner. In an effort to escape, Luke uses the Force to jump up to a grate above, but he is unable to get out and has his fingers mashed by Jawa gun butts for the effort. He then drops down right onto the Rancor's eye, causing it great pain... but again ends up on the run.
There seems to be no particular reason for this scene being cut, other than for time or because of the difficulty of the special effects regarding the fall onto the Rancor. It would have given another chance to see Luke exercise his Jedi abilities as he makes the jump to the grate.
A single photo from this scene has appeared in the Return of the Jedi storybook, and the scene is included in the novel as well.