Removing items from a Time Machine backup is designed to be done only from within Time Machine, presumably for safety reasons.
One thing I don't know however is whether or not time machine is savvy enough to deal with files and folders that are renamed and/or moved. Theoretically, this doesn't have to interrupt the linking process. In practice however, it greatly complicates making backups, as time machine attempts to identify what was moved or renamed since the last backup, so it can get the linking correct.
And now we may have the cause (which would be me
). A few weeks back I watched a conference on-line and, rather than take notes, recorded the event, which was saved in iMovie. As it turned out, I didn't need the recording after all and deleted it from my hard drive.
However, it was recorded in Time Machine and caused TM to stop making backups (which were now too large) even though the original had been deleted. So I thought I'd remove the recording from Time Machine. I went to
Time Machine>Backups.backupb>Dad's iMac and found a series of dated folders.
I "drag and drop" moved to Trash the folders that had dates which I thought would contain a backup of the original recording.