There was no secret mark printed on the Continental's 24¢ denomination. The sheets with a secret mark were indeed prepared, but they were never used. A the color of the 24¢ varies so much there is nothing to separate the National printed 24¢ (#153) from the Continental printed 24¢. Unless the stamp was printed on ribbed paper, which was used exclusively by the Continental Bank Note Co. A single example of the 24¢ on vertically ribbed paper has been certified.
The one and only #164 was last sold in 2004 for $325,000. The chances of you finding another are far less than the of odds of lightning striking you twice. However if you feel you have the trained eye to detect ribbed paper, and you have a 24¢ Winfield Scott on hard paper with the leaf fancy cancel on it, it might be worth investigating,
Purple ink at the time was a cursed color to work with. The carmine component of the purple was degraded by the heat in the drying room and from interaction with the acid of the gum. To add to the misery of producing this color it took longer than normal to dry. After much effort a purple was approved by the National Bank Note company. When the staff of the National Bank Company moved to the Continental Bank Note company they did not want to reinvent the wheel and carried on using the same ink that had been used at the National.
Ribbed paper describes the texture created by paper-making rollers that have fine corrugations cut into them. Ribbed paper can be confused with paper with heavy laid lines as their appearance when held to a light is similar. One way to determine if the paper is ribbed is to run your finger over the surface of the stamp, since ribbing is not a watermark but a texturing of the surface of the stamp.
Unlike laid paper ribbed paper cannot be detected in watermark fluid. The 'ribbing' on ribbed paper are forty lines per inch whilst laid paper is much more widely spaced. It can found vertically and less commonly horizontally. It was only used by the Continental Bank Note Company.
Hold the stamp at a very slight angle to your eye with a downward light source. Looking along the back of the stamp a trained eye can detect the vertical or horizontal lines in the texturing of the paper.
Photographing the ribbing of a paper is next to impossible. However above is an example of ribbed paper
Large die proof on India, die sunk on card
Trial color proof
Plate proof on India
Plate proof on card