You cannot delete your only inbox. If you have one inbox, you will need to create a second inbox, even if it's just using a fake name and email address. 

Once you have more than one mailbox, go to Settings → Channels, select the mailbox you want to delete, and click the trash can icon. 

A window will open and ask for confirmation to delete. 

⚠️Caution! Before deleting, please double-check that you don't need any of the tickets in the mailbox. Once it is deleted, all of the tickets in the mailbox will be permanently removed. If you need a hand moving your conversation tickets to another inbox within your Groove account before deleting, feel free to reach out to the Groove support team for assistance with this.