The first sort of thing we know about the teapot is owing to the logical constraint of inaccessibility: we know we can't know it, that any instance of learning associated with it must be causally disconnected from us and anything we can conceivably learn. It's absolutely external to our configuration space; there isn't a straight pathway through the world to such a teapot. But what does this mean?
One way to think of this is the problem of entanglement. At some fundamental level, any component of anything that's ever been interconnected "remembers" the other components, can theoretically be affected by its behavior independent of time or distance. So, the kettle can't be entangled with anything that could then be entangled with us.
We could propose perhaps that the kettle is in another cosmos; at any rate, somewhere radically inaccessible. But once granting the possibility of gaining knowledge about some theoretical larger metaverse, a "truly" inaccessible teakettle then would have to be not only in an entirely different cosmos than ours, but outside of any cosmos that could be conceivably interconnected with ours at any point.
I sense that we may already be straying beyond the bounds of your question, but I would speculatively suggest that the kettle would ultimately have to be considered as a kind of virtual particle. The kettle then would have to be walking a vacuum diagram -- somehow travelling backwards in time to causally found itself -- in order to truly minimize access.
Is it possible any longer to evaluate any claim about such a kettle? On my reading, no claim to knowledge can reliably be made -- except for our knowledge that it is outside of our knowledge-context. There amounts to a kind of fundamental paradox in making a claim to such "external context knowledge" as any in-context justification is impossible. The only justifications would also be external, and they in turn could not utilize any in-context justification. Indeed, the only way to justify this knowledge would be to render it in-context -- to directly demonstrate the inaccessible kettle.