It's most likely a wordplay on "termite", but how exactly did they come up with that is not known to me.
I'm pretty sure it's a combination of "thaumic", which is synonymous with "magical" in Terry Pratchett's books, and "nanite", a microscopic robot. So, it's a microscopic magic robot.
The other interpretation is that mite is for... mites. As in dust mites, except these are magical ones (thaum - ancient Greek for miracles or wonders, ala magic) that eat you.
I always thought of them in the second sense, ala termites. Since they are often referred to as bees.
