Hmmm.. IMHO, it depends on the forseeable future such a script will be exposed to. If you know you will change/add to the script again, I'd rather start using strict sooner than later... If that, however, keeps me from accomplishing my work at the time I planned, I'd chuck it, without second thought, too.
Regardless of that, if I'd inherit maintenance of someone else's obsolete script, the first thing I'd do anyway is to work through the code (most likely making lots of changes). And I'd be sure to cure it from overuse of local, no matter whether I use strict or not.
It's not about blindly obeying the strict dogma -- it's about bringing the script up to date.