The Burst SMS suppression list is called the Global Opt Out list or GOO. Any numbers added to the GOO list will be removed from any list on the system and cannot be sent to.
If you wish to migrate an existing suppression list from another system, you can simply upload the contacts to our GOO list as you would any other.
If a number is opted-out or added accidentally the only way to re-add is using the add single contact link on the list page. The system will then ask you to "Force" the re-addition of the contact.