The re-release of the DLC was announced on Bethesda's blog. They've also provided instructions for deleting the bugged version of The Pitt for those of you who downloaded it already:
Sign in to Xbox LIVE then press the guide button
Go to Settings->System Settings->Memory.
From here, scroll down to Fallout 3 and press A.
Select Fallout 3: The Pitt (Marketplace Content) press A then choose Delete, then Yes to Delete (make sure not to delete any of your game saves)
The Pitt allows players to travel to a new location, the ruins of Pittsburgh, filled with new quests, items, and foes. It costs 800 Microsoft Points ($10) and, to reiterate from previous articles, you won't have to pay again if you downloaded the glitched version yesterday.