じみた is a suffix-like expression that attaches to nouns to mean "looking like ~", "having the air of ~", or "tainted with ~". It conveys that something or someone has taken on a particular quality or appearance, usually with a negative or undesirable connotation. It suggests that the thing in question has become steeped in or colored by that quality.
じみた is the past/attributive form of じみる (a る-verb meaning "to become like ~"), so it functions as a modifier before nouns. The て-form じみて is used adverbially.
じみた most frequently appears with certain nouns:
しょたい所帯じみた – looking domestic/frumpy; having the worn-out air of a homemaker
としより年寄りじみた – looking old; acting elderly
いなか田舎じみた – looking rustic/provincial
じみた almost always carries a negative, disparaging, or pitying tone. It implies that the quality has seeped into the person or thing in an undesirable way. Compare this with っぽい or らしい, which can be neutral or positive – じみた is distinctly unflattering.
Attributive (before a noun): Noun + じみた + Noun
Adverbial (て-form): Noun + じみて
Predicate: Noun + じみている