'factory-tinted' is a compound of 'factory' + 'tinted'. 'Factory' originates from Medieval Latin 'factoria', from Latin 'factor' (from 'facere' meaning 'to make'), used in English to mean a place of manufacture. 'Tint' comes from Old French 'teint' (past participle of 'teindre'), ultimately from Latin 'tingere' meaning 'to dye'; 'tinted' is the past-participle/adjectival form.

'factory' developed from Latin 'factor' → Medieval Latin 'factoria' → Old French 'factorie' and into Middle English as 'factory' meaning a place where things are made. 'tint' moved from Latin 'tingere' → Old French 'teindre/teint' → Middle English 'tint', and 'tinted' formed as the past-participle/adjectival form; the modern compound 'factory-tinted' is a relatively recent English formation describing items tinted during manufacturing.

Originally 'tint' primarily meant to dye textiles or add color; over time it broadened to mean applying a shade to glass, film, or materials. 'Factory' shifted from notions related to an agent or maker to the place of manufacture; the compound specifically denotes that the tinting was performed during manufacture rather than aftermarket.