Time Machine backups still on drive, no longer in Time Machine

I have two computers backed up to the same drive, and I cannot backup Mac#2 because the backups of Mac#1 are taking up too much space.

On Mac#1, I went into Time Machine and used the Delete Backup option on several of the oldest backups. I ran into one problem (a bug, actually) in the process, which is that after you've done the first Delete Backup, when you do the second, the "Are you sure you want to permanently remove..." dialog box does not appear, and you have to just hit the Return key on your keyboard to proceed.

The second problem came when I saw no indication of any kind that the backups I was removing were really being deleted. So I exited Time Machine, and found a small window in my Finder showing progress bars for the processes of removing the backups — there were several of the progress bars, all of them "barber poling." I didn't realize how long the deletion of each backup would take, so assuming there was some kind of problem, I stopped progress on all of them, and went back into Time Machine to see if I did them one at a time, waiting in between, if that would help.

Once back in Time Machine, the backups I'd previously tried to delete no longer appeared, but when I go in the Finder to the externa drive's Time Machine Backups > Backups.backupdb > My MacBook Pro, the folders for those dates are still there.

Now, I suspect it would be a bad idea to remove these folders manually from within the Finder. But if I can't remove them via the Finder, and those dates no longer appear in Time Machine, how do I get rid of them?

Erasing and partitioning the drive are not an option at this point because there are other things on the drive, not just the Time Machine backups.