K Terminal on a Thermostat (Honeywell Wire Saver)
K is a combined fan-and-cooling signal used by the Honeywell wire saver (THP9045) and Amazon’s C-wire adapter. The module at the furnace splits K back into G and Y, which frees the old G wire to become a C wire.
Honeywell T-series and the Amazon Smart Thermostat understand K. Nest and ecobee don’t. Switching to one of those means removing the wire saver at the furnace and restoring the original G and Y connections (ecobee then uses its own PEK).