ホモテナシ

Either the host or the guest explain there'll be 続薄茶 instead of asking for おしまい. If the guest asks, the host will say that they'll relay the charcoal, to which the guest will say that'll not be necessary.

「お見受け（みうけ）　いたしますと、名水　を　御心配（しんぱい）　いただいた　よう　で　ございます　が、お水　を　頂戴（ちょうだい）　いたしたい　と　思います　」(I see you troubled yourself to get some famous water, so I would like to taste it).