Gramps manages the game's StreetPass functionality, allowing Link to setup a save file's StreetPass profile, which is named after whatever the player names Link. He also explains the nature of StreetPass to Link, and will allow Link to fight Shadow Links obtained from other StreetPass users.
After all 50 StreetPass challenges have been completed, Link may choose to fight Gramps whenever he wishes. He will have the maximum number of Heart Containers, all gear upgraded to maximum capacity, and two upgraded items. However, his bounty is a mere five Rupees; if he is defeated, he explains that this is because he offers bounties out of his own pocket to attract capable swordsmen and is not foolish enough to set a large one on himself.