Gift of mercy
From A Wiki of Ice and Fire
The gift of mercy is the term the Faceless Men use for the granting of a quick, humane death to a person who is ailing or mortally wounded and destined to die a painful, lingering death otherwise.
People may request the gift of mercy. For example, Osha grants the dying Maester Luwin the gift of mercy at his request, as does Sandor Clegane to a survivor of the Red Wedding, a bowman in service to Ser Marq Piper who escaped but was severely injured. Arya Stark gives the gift of mercy to a squire after a brawl at the Inn at the Crossroads, but denies it to the critically wounded Sandor after stating that he does not deserve it.