The offline ASG entry serves as a placeholder for where the real ASG would be in the tree. You cannot modify or delete the entry (although it is removed from the display if all of its child ASGs are deleted).
It is possible to delete the child ASGs of an offline ASG. However, it is recommended that you delete them only if the client for the offline ASG will never be put online again. It is best to delete child ASGs when the parent ASG is online.
If you choose to delete a child ASG, the operation is immediate. There is no need to press OK or Apply.