Would I be correct in assuming you're not actually restoring, but instead copying the backup files directly from backup storage to the target location? If so, you need to restore them using a Restore Plan instead. If my assumption is wrong, then please post the restore plan details.

No, I don't know how to copy.
I'm using the Restore plan / wizard. I select my AWS S3 account (using same access key used on the PC data was backed up from).
Below is the the summary of the restore plan. The back path on the original PC is "C:\Users\cvach\Desktop\No Backup\BCP" NOT "\\T430\C$\Users\cvach\Desktop\No Backup\BCP" as displayed in the Restore portion below (not sure if this matters).

Also when adding the AWS S3 account I chose in the advanced settings menu I chose "restore only" (but also tried "Regular mode" and selected the same backup prefix. Both ways yield the same end result.

Restore plan summary
Run restore once
Bucket name: XXXX-test
Backup prefix: DESKTOP-IKU0I31
Restore Type: Latest version
Restore:
\\T430\C$\Users\cvach\Desktop\No Backup\BCP

Destination folder:
C:\Users\T430\Desktop\delete\DR_TEST
Encryption: disabled

Notification options:
never send email notification

After running this restore plan on my test PC it placed the file in "C:\Users\T430\Desktop\delete\DR_TEST\BCP\Pictures\Lily.JPG$\20140215002812"

, how the files were initially backed up?
Looks like it was a backup to a local destination and then that destination was used as a source for cloud backup.
What you see is basically the file structure that we use for storing files on the backup storage. The numbers are a timestamp.
To get rid of this folders you can restore everything from the cloud and then use that folder as a source for one more restore job and restore files from there.

Please let me know if you need more details on how to restore it. And also try avoiding backing up backups.

Thanks

No, that was not it. These were not backups of my backups.

I did identify the issue - I was backing my data up using the CloudBerry 6.1.x and restoring on my older test PC where had previous installed CloudBerry Backup 5.7.3.

I installed CloudBerry Backup 6.1.3.9 on my test PC (this now matches the PC being backed up) and it worked. No more weird folder structure. I should have double checked version numbers.

, thanks for the update and the clarification.
Indeed, you can restore with no issues if the version with which you're restoring it is newer or the same as the one that was used for the backup.
Thanks