Scrope's Last Hope is a mission that coincides with Jackdaw's Rest. You'll find small notes left for you by the Black family house elf, Scrope, leading you to the coastline in the North Hogwarts region. He tasks you with finding a special family heirloom belonging to his late mistress Apollonia Black, and directs you to Jackdaw's grotto to find it. Nothing really comes of this mission except a little more quest time in the Forbidden Forest, but out of all the house quests this one does fit into the main storyline the smoothest.