When you are on the 'My Highlights' section of the mobile app and you have clicked into an event, you will see all of your highlights from that event. In the upper right hand corner you'll see a button titled 'Remove Event'. By tapping this, you will effectively remove that event and those highlights from the 'My Highlights' section.
If you have a Fantag Manager account, highlights will still be available in your account despite removing them from the mobile app.