According to Microsoft’s  MajorNelson, users who purchased and downloaded the DLC will have to   delete that version from their storage device before downloading the new version.

The necessary stepts are as follows:

– Sign in to Xbox LIVE then press the guide button
– Go to Settings->System Settings->Memory.
– From here, scroll down to Fall Out 3 and press A.
– Select Fallout 3: The Pitt (Marketplace Content) press A then choose Delete, then Yes to Delete.

The Pitt DLC pack can be downloaded once again at no charge. The pack costs $10 and includes new quests, items and new area to explore: a post-apocalyptic version of Pittsburgh.