Since there are several distinct questions within the original query, and other answers/comments seem to be focused on the aspect of funerary practices, this answer will focus on the OPs' question of artistic license by "the people making the movies".
The OP mentions the source of their question being 'EVERY version I have seen', we may be able to address whether this is
...a case of artistic freedom from either the people making the movies
...
by looking at the original text of Charles Dickens, A Christmas Carol (1843).
All citations below are from a copy found in the 1883 publication of Charles Dickens's Complete Works. (all emphasis mine)
From the early description of Marleys Ghost
No nor did he believe it even now Though he looked the phantom through
and through and saw it standing before him though he felt the chilling
influence of its death cold eyes and marked the very texture of the
folded kerchief bound about its head and chin which wrapper he had not
observed before he was still incredulous and fought against his senses
This item reappears more importantly in a later section, described then as a bandage, which the spectre removes to illustrate its dire condition in rebuttal to Scrooges' indigestion jest:
At this the spirit raised a frightful cry and shook its chain with
such a dismal and appalling noise that Scrooge held on tight to his
chair to save himself from falling in a swoon But how much greater was
his horror when the phantom taking off the bandage round its head as
if it were too warm to wear in doors its lower jaw dropped down upon
its breast!
This particular plot device makes one more appearance, as the Ghost is preparing to depart after having imparted its warning. This time the 'wrapper's function is spelled out clearly:
When it had said these words the spectre took its wrapper from the
table and bound it round its head as before Scrooge knew this by the
smart sound its teeth made when the jaws were brought together by the
bandage He ventured to raise his eyes again and found his supernatural
visitor confronting him in an erect attitude with its chain wound over
and about its arm
We can see from these passages that it was not merely artistic license by the movie makers, but was integral to the original story as written by Dickens himself.
We can even see a depiction including the bandage illustrated in artwork by John Leech which appeared in the first edition in 1843(Scanned image and text by Philip V. Allingham.):

So we can see that the aspect of the original query as to whether or not the movies depiction of this item is 'artistic license' by the movie makers is unfounded. The cloth around the head of Jacob Marleys' Ghost has been present since the story was published in 1843. It only is described as a kerchief, wrapper or a bandage; its purpose is implied in the text as holding the lower jaw in place. It is not artistic license 'by the people making the movies'.