here's the card: http://www.cardgamedb.com/forums/uploads/1285025507/med_gallery_1_64_124448.jpg

lets say the controller of the bastard's elite loses a military challenge as the defender. can he kill the bastard's elite to satisfy the claim ''before'' losing control of the card?

Resolving a challenge looks like this:

• 1a: Determine Winner of Challenge
• 2a: Save/Cancel opportunity against "Determine Winner of Challenge"
• 3a: Challenge is officially won (and lost)

• 1b: Challenge Result is Implemented (aka "claim")
• 2b: Save/Cancel opportunity against claim
• 3b: Resolve claim

• 1c: Reward for Unopposed challenge
• 2c: Save/Cancel opportunity against unopposed
• 3c: Unopposed power is claimed/put on House card

• 1d: Renown is awarded
• 2d: Save/Cancel oppotunity against Renown
• 3d: Renown power is claimed/put on character cards

• 4: Passsives (initiated by anything in 1a - 3d)
• 5: Responses (to anything in 1a - 4)
• 6: End Window

Claim is settled in 1b-3b, which is before control would change in 4.

that was unambiguous thank you