Also called the Imperial Intelligence Service, the Blades were sworn defenders of the Dragonborn Emperors and dedicated worshippers of Talos.
Long-time fans of The Elder Scrolls franchise likely recognized the Blades, an ancient organization first appearing in Morrowind. This suggests Paarthurnax's bounty stems from the Blades' desperation to control the Dragonborn and separate them from the Greybeards. However, the Blades do not ask them to kill Odahviing, Durnehviir, or other warmongering dragons to prove their loyalty to the organization.
The Elder Scrolls V: Skyrim's most heartbreaking quest asks the Dragonborn to kill Paarthurax at the request of the Blades.