There are rewards that you can unlock and then collect manually upon reaching specific Cup Points thresholds.
To see the Cup Points thresholds and their rewards: tap on the League symbol right above the Duel mode "PLAY" button (on the Main Menu screen).
Keep in mind that if you didn't claim your rewards after reaching a threshold, you will still be able to collect this threshold's rewards even if you have lost Duels and now have fewer Cup Points compared to the amount of Cup Points required to unlock the threshold's rewards.