How does the scoring work?

Score card? I think you are talking about your team member list. It shows their names and how many league ribbons that they have earned in total for the week from competitions, Help Wanted tasks, and Club Mystery rewards. The red button next to a member's name will remove them from the team. The red button next to an officer's name will demote them to member status. The green button will promote a member to officer. But be careful, if you promote an officer to president, you will also be demoting yourself to officer. You cannot reverse this yourself. The new president will have to do it.