I did not find a way in the GameKit documentation to delete a player's score from within my app. Is this possible?
Happily, Apple responded to the fake score problem and now there's a more convenient and efficient solution for managing fake scores compared to sending an e-mail:
Apple Announcement from October 28th, 2013: Manage Game Center Leaderboard Scores
You can now view and manage the top 100 scores and usernames for all of your Game Center leaderboards. Protect your legitimate players by signing in to iTunes Connect to delete fake scores or block players that post fake scores. You can also restore scores and players within the same time period. To learn more, read the Managing Game Center Leaderboard Activity section in the iTunes Connect Developer Guide.
Unfortunately, there's still no programmatic way to do this, but at least it's something.