I don’t have an answer but you may find more information from U.S.-based folks if you switch up your search terms. I’d never heard the term “grill(e) door” but “security door” turns up the search results I’d expect. There are likely other terms, too.
What @jrunning said, we would usually call them security doors, but also sharing a picture of what the lock area of the door looks like, jamb/frame side included would also be helpful
Well… The only thing I found until now is this “double” lock
Take a look at my door! You can see that there the glass can be opened (or worse, broken!) And then someone could just put there Han inside and press the “open” button.
How about a low-tech solution: Cover it up. You could use an off-the-shelf locking cover, like this receptacle cover or lock cover (google terms: “locking steel cover,” “security cover”):
It doesn’t have any hardware outside the door. It might work with your existing lock, or you could ditch the existing lock entirely and just cover the holes. I don’t have any experience with that specific product and reviews are mixed so YMMV.
You could also just buy a regular smart lock and remove the inside handle/knob. How easy or effective that is depends on the lock, of course.
I don’t think it is a good idea to use those locking covers. It would create such a difficult process to exit the house.
I also heard that some smart lock have a “night mode”. I wonder if this mode prevents the lock from opening from inside or if it prevents it to be opened from both sides.