To hide the Points and Tiers in the details panel on the side of the Competition, simply make sure ‘Show player stats’ is not ticked when creating, editing, or cloning a Competition.
The "Show player stats" option is available on the Gamification page.
This will hide the details panel for your competition (You can visually see the effect when you have checked/unchecked this option in the live preview on the right while editing/creating a competition.)
The other place that you can hide the Points is the Player Profile screen ( Tale Of The Tape).