The high score for each game in Ollie Soars can be independently reset.
 

To do so, tap the settings gear in the upper right corner of the lobby and then tap on the menu item for the game you wish to reset the score for. Finally, tap the "Reset Score" button. You will be prompted for confirmation, and if you agree, the game's score will be reset to 0 on all of your devices. There is no undo!
 

Unfortunately Game Center has no way to reset your own high scores, so this will only affect the score that is stored locally on your devices.