Ballantine's goal was to get the books in the shops quickly, to compete with the unauthorized Ace paperbacks, so they gave Remington very little time to work. She hadn't then read the novel and had little opportunity to find out anything about it, consequently this surreal and impressionistic thing came into being.
Tolkien, unsurprisingly, hated it. He erupted in dismay at the sight, and to the publisher's attempts at explanation commented, "I begin to feel that I am shut up in a madhouse." (A quotation I found singularly apt to use as an epigraph when I came to write on Peter Jackson.)
But to those of us who were weaned on The Lord of the Rings in the early paperback years (this cover was used from the first paperbacks in 1965 until about 1973), we imprinted on this bizarre artwork the way a baby bird will imprint on a plastic doll in the absence of its mother. The transition from a peaceful if inexplicable Shire (emus? pink bulbs?) to the hellhole of a blasted Mordor with what look like tissue-paper monsters writhing in front does, at least, convey the point Bilbo made to Frodo about the world they live in:
It's a dangerous business, Frodo, going out of your door. You step into the Road, and if you don't keep your feet, there is no knowing where you might be swept off to. Do you realize that this is the very path that goes through Mirkwood, and that if you let it, it might take you to the Lonely Mountain or even further and to worse places?