CTTH... or Closest to the Hole competitions have what is known as "potential best' ... the way it's supposed to work is that you will see your score in a little white box if that is the best you have done on that particular hole.
At the end of the round, if you scroll through your stats, you will see "Potential Best" as one of the scores.. it is possible to see a score of 0.00 in that stat, if you are like some of the best players here and have ACED every single hole.