Thanks for your advice, chuckebaby. It inspired me to experiment.
Apparently, if you drag in the timeline with no tracks selected, it automatically selects them all. If you've already selected a track, it doesn't do that. When it happened to me, I must have selected the area of the clip I wanted to delete but hadn't yet selected the track itself. I guess that's what you were trying to tell me.
The cleanup I was doing was removing the little noises before the playing starts (putting the bow on the string, etc.) and the clicks at the end of the clips when I stopped the recording.
Thanks again for your help.