Intuitions don't matter. If Mary can't activate her neural pathways participating in creation of experience of seeing red, then she has no means of knowing how she will experience redness. All models she can create in her mind will be external to her as the mind created by actions of human being in Chinese room is external to that human being.

And this limitation of our conscious understanding feels to us like a thing we have which cannot in principle be reduced.

It is not only conscious understanding that is required, we will need a conscious control of individual neurons and synapses to be able to experience qualia given just a description of it. For example, to be able to name color and imagine color given its name, Mary (roughly speaking) should manually connect neurons in her visual cortex to the neurons in her Broca's area and to the neurons in her auditory cortex.

So I think that, contrary to Dennet, Mary will get new information when she will see colors, as human's brain construction doesn't allow to acquire that information by other means. Thus in a sense human's qualia cannot be reduced.