The best example I can think of at the moment is Frankenstein’s monster from Mary Shelley’s Frankenstein. Many people know of the existence of this character well enough to allude to it (though usually erroneously by the name of its creator) at times when they see or imagine a grotesque being. However, if one actually knew the story, they probably would see more in the character than just its grotesqueness (despite it being a major trait, even in the eyes of Frankenstein the creator), as it has a story of its own. Yet most people (who I assume haven’t encountered the story in any comprehensive form) seem to remember the character only for that one trait alone, more than even its name. How do you describe a character like Frankenstein’s monster that’s popularly referred to but misunderstood or taken out of context? For example, “Frankenstein’s monster has become something of a ________ character.”
There is nothing wrong with the word "misunderstood" in your context. This website among many others uses the term "misunderstood characters". The term carries all the implications of hidden depth, better motivation, being more sympathetic than people think and so on that you want.
One word is caricature:
1 : exaggeration by means of often ludicrous distortion of parts or characteristics • drew a caricature of the president
2 : a representation especially in literature or art that has the qualities of caricature • His performance in the film was a caricature of a hard-boiled detective.
So, your example sentence would look something like:
The public image of Frankenstein’s monster has become something of a caricature of the actual character in the novel.
I always found it somewhat strange that while literature and art often exaggerate something from real life, in this case it's real life (and movies, another form or art) that is exaggerating something from literature itself.