Announcements can be deleted permanently from the business settings, once it is deactivated and it is not associated with any active campaign then it can be deleted.
Navigate to Campaigns > Announcements >> Click on the bin icon.
It is important to note that once an announcement has been sent to a guest, it cannot be deleted. You will know that the Announcement has been sent to guests as you will receive the notice "Cannot delete record because of dependent user_rich_notifications" when selecting delete. This is currently the intended functionality of this feature.
If further assistance is required, submit a ticket to Punchh Support. (For help submitting a ticket, click here)