There currently is not an easy way to reset the score in a challenge when it's over. However, there are a couple of options.
Let the challenge end and restart it. You will see a button for this. A restarted challenge will create a new challenge with all the same members and rules.
Take advantage of the "Club" group. A club automatically tracks the scores for every week and month. It's nice to use if you regularly create a lot of challenges every month.