George Lucas made a number of changes to the original Star Wars trilogy in 1997 and again in 2011, but the addition of Jabba the Hutt in A New Hope tends to fly under the radar compared to the infamous "Han shot first" controversy. Although the underworld boss was intended to make a cameo in the original release, Jabba's presence makes absolutely no sense in the movie, and his scene should've remained on the cutting-room floor.
During the original filming of A New Hope, a scene was shot that depicted Jabba the Hutt confronting Han Solo in the Mos Eisley docking bay that housed the Millennium Falcon. A stop-motion creature was supposed to be added, but it was cut due to time constraints. In the 1997 edition, a CGI Jabba was added alongside a team of bounty hunters, including Boba Fett. Jabba questions Han about his missing payments and asks about the death of Greedo in the Mos Eisley Cantina. Solo says he'll have Jabba's money, with 15 percent interest, and the Hutt simply lets the smuggler leave after threatening to place a bounty on his head if he misses another payment.
The most apparent reason this scene doesn't make sense is due to the prior confrontation at the cantina. Greedo was sent by Jabba to kill Han, meaning the smuggler was already a wanted man during their confrontation. Because Greedo shot first in the re-releases, it's safe to assume the contract called for Han dead or alive. By the time Jabba got to the Millennium Falcon, Chewbacca and Han were heavily outnumbered by the gangster's bounty hunters. The crew easily could have taken down or captured them if the Hutt wanted them alive. As Jabba mentioned, Han wronged him twice: once by abandoning cargo and another by killing Greedo, meaning the Hutt had no reason to trust the smuggler would pay his debt.
Jabba's assertion that he is coming for Han's head is also puzzling, as it again implies he was wanted dead or alive. That's in contrast to the events of The Empire Strikes Back, however, as Fett was anxious about the carbonite freezing process killing Han, which would hurt his bounty.
The scene also doesn't track from Han's perspective, either. His approach to their meeting was too casual, as he stepped on Jabba's tail and insulted the crime boss by calling him "a wonderful human being." While Han may have intended to clear up things with the gangster before leaving Tatooine, he would have more likely done so be paying a visit to Jabba's Palace, rather than relying upon a chance meeting in a hanger bay. Han had no reason to believe that Jabba would be waiting, relatively peacefully, outside the Millennium Falcon, especially following the confrontation with Greedo.
The inclusion of Jabba the Hutt in A New Hope contradicts Greedo's showdown with Han, as well as the events of The Empire Strikes Back. A New Hope functioned perfectly without the addition of this scene, which served as nothing more than a glorified cameo.