Thanks for the hint and here we seem to have part of the story:
"Gene liked the artwork, and had me show it to the art director, Matt Jefferies. Jefferies bought about twenty pieces to use as art objects around the ship. Some of the critters were hanging in McCoy's office and cabin during the third season."
Unfortunately a Google search didn't yield any real visual results, except the Trekcore links to this thread.
So do we at least know what these landscape paintings were supposed to show? Ruins or remains of ancient civilizations?
And do we know anything about the "tags" that apparently show up in every painting's lower left corner?