How do I return an external backup hdd to its original new state?

As you have probably discovered, Disk Management won't let you delete that recovery partition.

From a Command prompt (Admin) use DISKPART

At the DISKPART> prompt, list the disks to identify the disk number to use, then...

Code:

DISKPART> LIST DISK

  Disk ###  Status         Size     Free     Dyn  Gpt
  --------  -------------  -------  -------  ---  ---
  Disk 0    Online          465 GB      0 B
  Disk 1    Online          931 GB      0 B

DISKPART> SELECT DISK 1

Disk 1 is now the selected disk.

DISKPART>CLEAN

The CLEAN command removes all partition info from the selected disk (obviously I didn't hit return when generating the above example using my own ext HDD :))

Once cleaned, the disk will appear as 'unallocated'. You can use the Diskpart command CREATE PARTITON PRIMARY to create a partition using the whole available space, or use you usual tool of choice.

It's not a forensic clean, so it won't securely erase the disk, just removes all partitions. If you need to do that, use CLEAN ALL but it will take quite some time to complete.

Code:

DISKPART> help clean
     Removes any and all partition or volume formatting from the disk with
     focus.
Syntax:  CLEAN [ALL]
    ALL         Specifies that each and every byte\sector on the disk is set to
                zero, which completely deletes all data contained on the disk.
    On master boot record (MBR) disks, only the MBR partitioning information
    and hidden sector information are overwritten. On GUID partition table
    (GPT) disks, the GPT partitioning information, including the Protective
    MBR, is overwritten. If the ALL parameter is not used, the first 1MB
    and the last 1MB of the disk are zeroed. This erases any disk formatting
    that had been previously applied to the disk. The disk's state after
    cleaning the disk is 'UNINITIALIZED'.
Example:
    CLEAN
DISKPART>

Bree's solution is straightforward and effective.

An additional option for future reference: Since you now have MiniTool Partition Wizard as evidenced in one of the many threads you have open around this (I assume related) issue, you can simply use it to remove partitions also.

Or since you are in the Disk Management, right click the G: drive and the Recovery partition and Delete them, until the whole drive is Unallocated Space.

spunk said:

Or since you are in the Disk Management, right click the G: drive and the Recovery partition and Delete them, until the whole drive is Unallocated Space.

Recovery partitions are usually protected in Disk Management, the only option with a right-click is 'Help'.