Perhaps some stories involve the challenges faced at the first tee. For example, a golfer might have been really nervous and had to overcome that to make a good shot. There could also be stories about the beautiful scenery around the first tee that inspired players. Another aspect could be the friendly competition that starts right at the first tee, with players joking around yet still being competitive.
In 'Pulp Fiction', Jules is a character. Maybe a tee shirt could be related in that there could be a tee shirt with Jules' image on it, or perhaps Jules was wearing a particular tee shirt in the movie that became iconic in some way.
I don't know the main characters as I've not come across this story. But if Tee is in the title, Tee might be one of the main characters, and of course, the snakes are likely to be important characters as well.