If they’re actually trapped in an invisible box, are they even mimes?

Do not breach MIME* containment at any cost

*MIME - Massive Interplanar Mortality Event

Do not, under any circumstances, release the mime.

… what if they are protecting themselves from us?

Yes? Yes. They trap themselves in the box with their barrier magic for show, and sometime one might used too much magic for that so a Meteor has to be casted on them.

No, I agree with Vetinari on this point