Orders are refunded from within the Baby Bunting Marketplace. Omnivore does not send a Refunded order status to your eCommerce Store.
So if you need to refund or cancel an order it has to be done in Baby Bunting, see here:
Then in Omnivore manually.
Open Omnivore - Go to 'Orders' in the left hand navigation - Find the order and click through to the page which holds all the order information - Click 'Mark as refunded'.
Then depending on your eCommerce Store if the order is in your store following the relevant instructions to cancel and refund the order.