For starters, the tape is to keep up with whether or not that tine has been scored yet. It is also used at the base of tines to gather a point of origin to begin measuring length of a tine.
The person in the picture doesn't work near the county that this was found and he is not a game warden, so I find it odd that he is holding it and it came from that county. Not saying it didn't come from there, just curios as to why he is referenced in the pictures. I am sure it is for unofficial green scoring since there is no such thing as an "official green score"
It did come from Carter Co. I believe the gent in the pic did the scoring.