Using your team’s Definition of Done’ (DoD), a Story is either done or not done. Period. No points credited to the team for that iteration for the perceived percentage of the ‘Done’ part of the Story. That story goes back to the backlog to be reprioritized with the rest, replanned, and resized (as a result of earlier work, more is now known and complexity lessened).
The reason why people are so anal about receiving credit points to partially done Story is their quest for a favorable outlook of their own predictability ratio… which is the total points accepted divided by the total points committed. They are just fooling themselves — gaming the system — by taking credit from unfinished job (story).
FedEx has high predictability ratio. The movie ‘Castaway’ is proof ;-). The character (played by Tom Hanks) finished the job… he eventually delivered!
Pain is good. Take that hit for not having the ability to complete that story… it is a learning moment!
It provides the real narrative of the predictability and volatility of your team’s delivery… look for improvement items… aim to be better next time.