Give me a case where this is a useful distinction.

The intended use is to tell us whether neuroscience is complete.

It's possible that her ability to predict her own surprise won't involve an ability to predict what she is surprised at, how red looks.

This is exactly the useless distinction, right here. You're drawing a distinction between knowing how red looks, and being able to act as if you know how red looks. (Being able to predict her surprise vs being able to predict the look of red). In practice, everywhere, there is no difference.

That is a bold claim. Surely there is a subjective difference between predicting the surpise, and predicting the red? Or are you looking at it behaviouristically, from the outside?

The only use of knowing how red looks is to check that your model of neuroscience is accurate, and we've already specified Mary's knowledge is complete.

No. We have specified that it is descpriptively complete. The whole point of the story is to explore whether complete descriptive knowledge is complete knowledge.

You are saying that Mary would know what red looks like while on the room? I''m not sure if I am

It would be helpful if you were sure.

The way I phrased the question, I think that saying "yes, she experiences the qualia of red" means that she knows what red looks like while she's in the room, and saying "no, she does not experience the qualia of red" means she doesn't know what red looks like while inside the room.

So which is it?

I would be greatly honored if you could quickly outline what work you feel that qualia does - what theories does it support, what does it count as evidence against, what does it rule out and what does it prove, what impact does it have? What does it mean, if qualia existed?

That qualia exists means there is something lemons taste like, and saxophones sound like and sunsets look like. Beyond that...why do you need to know? Are you planning to deny that there omething lemons taste like, and saxophones sound like and sunsets look like if it leads to implications you don't like?