When ready enter the building and start going around (you don't need to speak with the girl). Once you reach the other side constables will come to attack you, and this is very much like a kill 100 type mission as you need to kill 25 constables before the flow stops. Once you're done head back into that house's area and pick up the purple furoshiki.
If you do like I did once and forget to pick up the purple furoshiki after killing the constables, go into menu, journal and missions and fully cancel the mission. If you just re-kill the constables after exiting the area the purple furoshiki will not drop.