Solution Below.

1) Logoff all users from the project.

2) Request the DBA perform a backup of the project database.
THIS IS CRITICAL in the event the repair process is encounters an error during the process.

DO NOT PROCEED WITHOUT a confirmation from the DBA that the backup has successfully completed.

3) In the Site Administrator

a. Select the project name

b. Right click and select the Maintain Project / Verify Project / click the [Verify Project] button.

This will create a file in the directory
C:Program FilesHPQuality CenterrepositorysaDomsInfoMaintenanceDataoutDEFAULT\ default__db_trees_xxxxxxxxxxxxx.txt file.
Contents similar to:
Ids of items with bad paths: [123,234,456,111,222,333,444]
These are the requiment Ids with an issue.

c. Right click and select the Maintain Project / Verify Project / click the [Repair Project] button.

d. Click [Yes] to agree to deactivate the project.
This will rerun the verify process followed by the repair process.
If successful the message Repair finished successfully will be displayed.

4) Login to the project

5) The Requirements are listed in the correct tree path.