I screwed up manually deleting TimeMachine backup

Never manually delete Time Machine files or directories from the Finder. Time Machine makes heavy use of directory hard-linking, which the Finder doesn't really handle correctly. Chances are your backup is damaged now, making the safest option being a wipe of your backup disk, and making a new backup.

I manually deleted all backups by dragging the contents of my backup external hardrive into the trash

Yep. BIG mistake.

Since your intention seems to be to erase the backups, go to Disk Utility and simply format the Time Machine drive. Takes 20 seconds.

You can ignore the trash, it will disappear after the reformat.

The answer involves the command bypass. If you really want to delete files and/or folders (directories) from Time Machine (or anything else), this will do it.

In my case, I needed to remove Time Machine files from a external disk that contained other files. I could not simple reformat the partition.

The command bypass is hidden relatively deep in OS X. In Yosemite, the full path to bypass is shown below.

/System/Library/Extensions/TMSafetyNet.kext/Contents/Helpers/bypass

Since this is a fairly long path, I suggest when first opening a Terminal application window, enter the command shown below to create an alias.

alias bypass=/System/Library/Extensions/TMSafetyNet.kext/Contents/Helpers/bypass

Now. if you really want to show your computer who is in charge, enter the remove command as follows.

bypass sudo rm -rf name

Here, name can be either a file or directory. Be warned, this does not put anything in the Trash. The file or directory is permanently deleted. If used on a directory, the action is recursive.