The short answer is that you will need to erase that TM backup drive, but before you do that back out of that first screenshot that shows the contents of "MacBook Air":
Next, open that Backups.backupdb folder. It should contain one and only one folder within it, bearing the name of the Mac it's backing up.
Since that screenshot only shows the contents of "MacBook Air" I cannot be certain it is the only folder within Backups.backupdb. If there is another folder within it, that would be the redundant one I speculated might be present. Collapse the "reveal triangle" adjacent to "MacBook Air" to determine if another backup of that Mac is present, under a different name.
If that's the case, you would need to erase the drive anyway because Time Machine "owns" that drive and everything in it.
It gets worse though, because if you manually erased backups using the Finder (which is not clear to me yet) it's very likely the TM database was rendered invalid and and unusable for purposes of restoring an entire system. At best it should be considered unreliable, and an unreliable backup is worse than none at all.
So, my recommendation is to obtain another TM backup drive, create a new backup with it, then erase the existing drive. Not only are external drives inexpensive, one and only one backup device isn't a robust backup strategy anyway. A 2 TB drive will cost only a few dollars more than a 1 TB drive. Time Machine will back up to both of them — or as many additional drives as you may want to give it — in a "rotation" fashion. If one backup drive isn't available, it skips to the next one, and so forth.
By the way get rid of any Western Digital's drive "manager" or "utility" software that they are fond of bundling with their products. They are not required, and using them has been known (in the distant past) to have corrupted perfectly good drives. I mention that only because there is a mounted "WD Apps" volume on that Mac. The first thing anyone should do with any external drive is to format it with Disk Utility. That accomplishes two objectives: it prepares the drive for use with your Mac, and it gets rid of the junk software that may be on it.