This seems a bit silly really, but every single discussion of cast-iron cookware begins with "Seasoning your cookware", yet I've never heard of seasoning a cast-iron teapot. Is there a reason for this? Should I have been seasoning the things this whole time? Assume they're not enameled, and I use them to brew tea but not to heat water.
You can season the exterior of the kettle to help prevent rust, if you like.
The interior of a cast iron tea kettle is often rust-proofed through chemicals that accrue during normal use. One of these is lime scale. Repeatedly boiling water, especially hard water, will build a coating of lime scale that will keep rust at bay.
Another set of chemicals that help reduce the occurrence of rust are tannins. The tannic acid in tea leaves will react with red iron rust on the kettle to produce a more stable, blue-black compound called ferric tannate. To "season" a brand new tea kettle you can save used tea leaves and bags then place several in the pot and adding boiling water. Allow the "tea" to sit for 20 minutes then discard and rinse.
As other answers state, a traditional fat-polymer seasoning of the interior is unnecessary because you do not need to prevent food from sticking to the kettle.
The reason for seasoning is to prevent foods from sticking while cooking. The polymerized fats that constitute the seasoning layer provide an extremely slick surface which doesn't bind well to foods, so sticking is vastly reduced.
None of this has applications in a tea pot, where sticking is not a concern, so seasoning is not necessary.