Kas finds somewhere slightly reasonable to put the letter.

He eats his muffin.

He changes his clothes.

He puts Isabella's alethiometer downstairs at the Janepoint and makes the room impassable and its contents inviolable to anyone but himself and his girlfriend.

He packs his own alethiometer in a little backpack, and closes and locks the door, and pins a note to it: Isabella Amariah is gone on important business and may be some time.

And then he teleports to a random city on the same continent.