First, you will need to click in to the area you wish to remove the product group from. Beneath the product groups added to this area section, you’ll be able to see all the product groups in your area. On each product group's row, there is a red cross. When you click this, this product group will then be removed from your area.
Now that the product group is out of your area it will be back among your other product groups in the add product groups drop-down menu.