I did a search for Karl Mark's Pizza in Moscow Idaho, and was happy to find your site.  I have told people about it for years, but I could find nothing of it.

You mentioned that they spelled it "Mark's" instead of "Marx".  When I visited the place in 1984, I made the same remark to the lady taking my order, and commented on the irony of "Karl Mark's Pizza" in Moscow.  She laughed, and said that she never thought of that before, and that it was called "Karl Mark's" because one of the owners was named "Karl" and the other "Mark".  Thought you might find that somewhat interesting.