You can't erase or delete any 'Recent' configurations. They are just the last 5 configurations that you used to generate sight reading exercises. So as you generate new music with different configurations, the older ones will be pushed out of that table and the new configurations will populate the table.
To delete a 'Saved' configuration, go to the 'Sight Reading' tab on your Dashboard and click 'Saved' to view your saved configurations. Click the garbage icon next to the configuration you want to delete.