'anime-influenced' is a compound formed from 'anime' and the past participle 'influenced'. 'anime' originates from Japanese, specifically the abbreviated form of the English word 'animation' ('アニメーション'), where it meant 'animation'; 'influenced' originates from Latin via Old French, specifically from the verb 'influere' where 'in-' meant 'into' and 'fluere' meant 'to flow'.

'anime' entered English in the mid-20th century as a borrowing of the Japanese short form of 'animation'; 'influenced' came into English through Old French 'influence' from Latin 'influentia'. In modern English the two combined as the compound 'anime-influenced' to describe things showing influence from anime.

Initially, 'anime' meant 'animation' in Japanese and 'influenced' originally referred to being affected (literally 'flowing into' from Latin); over time the compound evolved to mean 'showing stylistic or thematic influence from anime' in contemporary usage.