relic of a past age; museum piece; something hopelessly outdated
Figurative expression for a person, idea, or thing that is seen as belonging to a bygone era and no longer relevant. Often used critically or humorously.
His way of thinking is a relic of the last century.
This old machine is truly a museum piece.
時代遅れ is an adjective/noun meaning 'outdated' or 'behind the times', while 前世紀の遺物 is a more vivid, metaphorical phrase literally meaning 'relic of the previous century'.
Compound of 前世紀 (previous century) + の (possessive particle) + 遺物 (relic, remains). The phrase is a straightforward metaphor, not historically derived from a single classical source.