Thank you for your speedy reply.
That's right: the Analytics code is already in the template, not in an editable region.
Why would this arbitrary snippet show up in an editable region, when it is not in the template there or in the library item? It's somehow pulling a part of the Analytics code and putting it in again?!? (This only occurs when I apply the template to an existing page.) Doesn't make sense to me...
I would honestly just be speculating, as I don't really use templates, myself. My guess would be that it's being referred to in some other way in your template, that makes it think you still need it. I'd check references for your scripts and the like to make sure there aren't any duplicates.