How to delete Found.000 directory and subdirectories?

I'm facing a rather strange situation.

I have a directory on an external hard disk named found.000. Its attributes are Hidden and System. Inside it there is another directory named dir_00000000.chk. That one also has Hidden and System attributes.

Now it's worth noting that in Windows Explorer the dir_00000000.chk directory is not shown, but I do see it with Total Commander.

My problem is that I cannot remove these directories from the external hard disk. I tried various methods as Administrator, but the weird thing is that Windows informs me that I need a standard user account's permission to delete the dir_00000000.chk directory. I tried removing the two directories directly from an Administrator account as well as from a standard user account.

I do not want to format the external hard disk because it holds my backups. Is there a way to remove those directories after all?

EDIT: I don't know if this will help, but I delved into the Security settings in file properties and I got this message for each of the files below:

An error occurred while applying security information to:

M:\found.00000000.chk\IndexerVolumeGrid
M:\found.00000000.chk\MountPointManagerRemoteDatabase
M:\found.00000000.chk\tracking.log
WPSettings.dat

Failed to enumerate objects in the container. Access is denied.

The above appeared separately for each of the four entries. I had to press Continue in each case.

I went to the second link that you gave me. I had seen it earlier before posting here, but there was no success in running cmd as Administrator. I'm guessing that after I played around with the Security settings, probably the one about enabling inheritance, made it possible to run cmd as Administrator and enter the dir_00000000.chk subdirectory. In there after some effort within other subdirectories that I discovered and finally having to change file attributes in some cases, I manged to delete everything. The whole process took me 8-10 minutes.

To make certain that everything is fine I rebooted the PC and so far I don't notice anything unusual.