ex gratia
adjective, adverb formal uk/eks ˈɡreɪ.ʃə/ us/eks ˈɡreɪ.ʃə/
（尤指并非出于法律义务而）作为恩惠的，出于善意的，出于帮助的
An ex gratia payment is not necessary, especially legally, but is made to show good intentions.
Ex gratia payments were made to all those who had been affected by the spillage. 受到泄漏事故影响的所有人都得到了额外的补偿。