These pieces are marked with a bright CNW logo - dead center on white china. These are not so much counterfeit pieces (because they copy no real pattern), but rather toys. They do slightly resemble some CNW lunch counter patterns, but those pieces are marked as such. Alas, unscrupuous antique dealers often try to palm these off as "vintage" pieces. They must have been made by the shipping container full, as they exceed the level of common. The only piece I recall seeing is the shown single egg cup, but it is possible that other small pieces exist in the set. They truly have NO value, except as toys or to dupe the unknowing.
(Note: The use of the word "counterfeit" to describe this china is not meant to imply that it is "good" or "bad" - for our purposes, the intentions of the counterfeiters are irrelevant. Authentic dining car china was made to be dining car china, counterfeit china was made to look like dining car china. Well done or not, it is not authentic dining car china, and if it is not clearly marked as a reproduction, then it is counterfeit.)