let's punt the call
In American football, the team controlling the ball must surrender control to the other team if they fail to move forward 10 yards (meters) in four attempts. Usually, if they fail to advance 10 yards in the first three tries, then they will choose to surrender control by kicking the ball to the other team far down the field. Otherwise they risk surrendering control to the other team much closer to that team's goal line. That type of kick in American footbal is a "punt". https://youtu.be/E_ZBAiE3rVQ
Away from football, the word is used figuratively to mean to abandon any sort of activity, an anology to the football team choosing to abandon, for the time being, their control of the football.
We Americans love sports references. In this case, it's from American football.
It means to delay or postpone (to another time).