Ah, sorry, I should have made that clear: yes, this is just in the Quixe interpreter. It doesn’t happen in the IDE or with Lectrote. (I updated the title of this post to rectify that oversight.)
In fact, I’m using the custom “Quixe-with-stylehints” that you provided here: [I7, Glulx] Retaining Text Style Settings in Web Interpreter.
The current class curriculum has the teachers clearing the screen. The problem also happens on a restart but they don’t plan on restarting the story files all that much. The clear screen is being used so that they can more easily show concepts without clutter.