Customer groups can be deleted from the register. To delete a customer group, log in to the Loomis—Pay administration panel and go to Customers > Customer Groups. Click Edit on the line you want to delete, and then Delete (red button).

The customer group is not actually deleted, just hidden. Loomis—Pay does it this way to preserve statistics. The customers linked to the customer group will be preserved, but any discounts for the customer group will not apply to future sales.