The spellings blood price and blood-price are both used in the books.
A blood price is a Kencyr concept regarding revenge for the slain.
Traditionally, a blood-price is paid by a member of the slain's house killing their killer. It can also be paid through gold, or though other arrangements. Blood prices can also be waved, the the slain's family doesn't deem it necessary.
Blood prices are demanded by the slain's family, and if the dead's family is all killed as well, blood prices are rendered somewhat irrelevant. In the Kithorn massacre, after one Kencyr was killed, the Merikit killed everyone to try to stop the Kencyr coming after them for the blood price. Blood prices cannot be demanded if both the victim and killer are of the same house, though maternal blood-kin of another house can demand blood prices as well.
At Tentir, if a cadet is killed, their house cannot claim their blood price. This may only count if both the victim and killer are at the college; after Anise is killed by Noyat raiders, Jame refers to her killer's death as Anise's blood price. Since Jame did not actively hunt the Noyat, however, the no blood prices of any rule kind might still be how it goes.
In lieu of formal blood-prices, other types of challenges may be made instead.
↑Dark of the Moon, "Chapter 2: The Hell Hunt" — " 'Afterward, he hunted the Merikit and killed one for each member of his lord's family and his own to pay the blood price.' "
↑Dark of the Moon, "Chapter 4: First Blood" — " 'I killed that boy. I don't even remember it […] Caineron's cousin…' […] 'The blood price must still have been ruinous.' 'Oh, it would have been if I had paid in gold— […] I gave my word that the next time the Host gathered, the entire High Council would have to consent before it could march out of the Riverland. […] It was either that or order you to use the White Knife instead of forbidding it.' "
↑ 3.03.1Dark of the Moon, "Chapter 10: The Lurking Past" — " 'Ardeth… […] I've just killed your cousin, or maybe Korey has. As maternal blood-kin, what blood price do you demand?' 'What price? […] Why, none, my boy. I saw everything. It probably was an accident.' "
↑Seeker's Mask, "Part I", V — "What did it matter if the blood price for the slain went unpaid when no Knorth were left to collect?"
↑Seeker's Mask, "Part VIII: Kithorn" — " 'But the Merikit hall-guest who opened the gate cut the throat of the Kendar guarding it,' […] 'They knew that there would be a blood-price to pay for that, and they panicked. The barracks was sealed and set ablaze; the tower, stormed; the people—men, women, and children, Highborn and Kendar—slaughtered. […] And then, despite it all, the price fell due, because they'd missed someone.' "
↑ 6.06.1Bound in Blood, "Chapter XII: Fire and Ice", III — " 'I say this now: come down, and bring with you whatever weapon you choose. No blood price can be demanded here at the college, certainly not within the same house, but I challenge you, Vant, for failure to obey orders, resulting in a cadet's death.' "
↑Seeker's Mask, "Part VIII: Kithorn" — " 'The college has its own rules. If you're hurt there, I can't even demand your blood-price.' "
↑Honor's Paradox, "Chapter XVIII: Summer's Eve", I — "the Noyat who was backing away with open mouth […] Behind him, the water seethed obscenely with blackheads. […] Round holes appeared in his pale skin and leaked red around the thrashing black bodies as they bore into him. […] Jame […] watched steadily as the blackheads claimed Anise’s blood-price."