This is something that has bugged me for ages but I have finally found out how to clear them (courtesy of Pinside). There is no option in the adjustments to clear tournaments but this is how you do it.
You have to start and stop a tournament 10 times. This will then clear all tournament scores.
Go to the Tournament settings from the menus and Quick Start a Tournament. Now if you keep pressing the Select (black) button the tournament will start and then stop. Do this 10x and all the Tournament high scores will be cleared. A bit clunky but it does work.

You have to start and stop a tournament 10 times. This will then clear all tournament scores.
Go to the Tournament settings from the menus and Quick Start a Tournament. Now if you keep pressing the Select (black) button the tournament will start and then stop. Do this 10x and all the Tournament high scores will be cleared. A bit clunky but it does work.
