It sounds like your P2 media isn’t associated with a project.
How are you bringing it into the Avid? If you open a project and consolidate it off the cards it will be associated with that project. If you’re just doing a file transfer at the desktop level then importing the Master Clips they’ll be orphan media.
The only way I know to stop the P2 files from showing up in every project in the Media Tool is to associate them with a project. That means consolidating off the cards when you first bring the footage in or doing a file transfer, selecting all the clips, and consolidating them–deleting the original media (so you don’t have duplicates). The latter is time consuming, yes, but should solve your problem.
Michael.