Given it was a quote found in the OT anyway, why bother removing it now? Because if they did not see the "name" Melchezedik there (so many years ago) but gave themselves the liberty to add it (then) I cant tell what they are doing. How'd a name like that accidently appear in the text, but all the sudden the ink of it vanished (or something?)
They bothered because it's the job of translators to give the best possible translation of the Greek. Do you really want them to say "let's not bother getting this right?"
There are *lot* of manuscripts of the Bible, so scholars have plenty of opportunity to see what kinds of errors copyists make. In many cases it's obvious which reading is right, because it's just one copy. There are certain standard types of error. One common one is that when two verses end the same way, the scribe's eye goes to the wrong place on the page and skips from one verse to the other.
Another common type of error is that when similar texts appear several places, the scribe remembers the other one. E.g. Matthew and Luke are very similar. There are times when a copy of Luke ends up with the wording from Matthew or visa versa. That's almost certainly what happened here. The scribe copied verse 21 but remembered the ending from 17.
Remember, the way copying worked, either the scribe had to read one copy, and then move his eyes to the other one, remembering what he had read, or someone else would read the document while the scribe wrote. These processes both have dangers, although they're somewhat different.
So we have a number of early copies where 17 and 21 end differently, and late ones where they end the same. Most scholars would conclude that it's much more likely that someone remembered 17 and thus made 21 look the same, rather than the opposite theory that someone dropped the reference to Melchisedek in 21 in the early copies. Judgements like this are based on all kinds of things, e.g. which types of error are most common, and which manuscripts are known to have which kinds of errors. E.g. apparently it's more common for scribes to add words than the remove them. That's one reason that recent texts are often slightly shorter. It's not that we're omitting things, but that we're correcting errors, many of which added things.
This kind of judgement always has to be made. The KJ is based on this kind of thought process as well. The person who put together the Greek just didn't have access to as many Greek manuscripts, nor to manuscripts as old as we have now. Partly because there weren't as many manuscripts available, the practice of reconstructing them wasn't as well developed in the 16th Cent as it is now.
It's kind of ironic, actually. The KJ is largely based on a Greek text by Erasmus, a well-known humanist working in the 16th Cent. But he really didn't intend to produce an authoritative Greek text at all. His goal was to produce a new and better Latin translation. In order to do that, he had to come up with a Greek text to start from. He published that text with his Latin, so that others could verify that his Latin translation was correct. Unfortunately his editing was rushed, probably because of publication deadlines. He also had a tendency at times to use the Latin as the basis and translate it back into Greek, though I doubt that that's the case here. He succumbed to pressure in one case. His initial version omitted 1 John 5:7-8, on the quite reasonable grounds that it wasn't present in any of the Greek manuscripts he had. It had entered the Latin in the 6th or 7th Cent as a "gloss". That is, someone apparently added it as a comment in the margin, but eventually some copyist mistakenly put it in the main text. But for a later addition he gave into pressure and accepted it. (There are some stories about how that happened but I'm not sure they are reliable.) This is one of the known ways that extra things sometimes entered the text. It's another reason that modern texts are sometimes a bit shorter than the KJ. We've got better evidence now and can often detect things that entered as glosses.
Again, his Greek was a great advance. Previously the Church had been using a Latin translation that had lots of errors. His new version fixed most of them, and is considered one of the reasons for the Reformation. But it is certainly not perfect.