First, FWIW: the search string:
grep -a -i -r "Linux" /media/hd/doc/computer/
also comes up empty. Thank you, though, berndbausch, for suggesting that the string might be stored differently; I hadn't thought of that.
This page at serverfault told me I can grep my way through binary files with the -a
Did I misunderstand something? (Wouldn't be the first time ...)
I'll experiment with catdoc, syg00; thank you for this recommendation.