jeomwoni jarireul jeongrihaneura neutge wasseo.

-이/가 marks the grammatical subject. 점원이 says the clerk is the doer of the actions (tidying, coming late).
Using 점원은 would make the clerk the topic, often with a contrastive nuance (as for the clerk…), e.g., implying others might have been on time. Both are possible, but 점원이 is the neutral, matter‑of‑fact choice here.

-느라(고) means because one was occupied doing X, Y happened (typically an undesirable or excuse-like result). It often carries a nuance of being tied up with the first action.
Example: 공부하느라 전화를 못 받았어 (I couldn’t answer because I was studying).

With -느라(고) you attach it to the verb stem (non‑past) to describe an action in progress that causes the result. 정리했느라 is ungrammatical.
If you want a completed‑cause nuance, use something else: 정리해서 늦게 왔어 or 정리하고 늦게 왔어.

자리 means seat/spot/place. In restaurant/shop contexts, 자리를 정리하다 typically means to clear/reset tables or tidy the seating area.
The -를/을 marks it as the object of 정리하다. In casual speech, you might hear the particle dropped: 자리 정리하느라…

• 늦게 왔어: literally came late (adverb 늦게 modifies 오다).
• 늦었어: was late (predicate adjective).
  Both are common; 늦게 왔어 focuses on the act of coming; 늦었어 is more general.

왔어 is casual/informal. Politer options: 왔어요 (polite), 왔습니다 (formal).
If you want to honor the subject, use honorifics: 점원분께서 자리를 정리하시느라 늦게 오셨어요.

• -느라(고): tied up doing X → inconvenient Y; same subject; no commands/suggestions in the result clause.
• -아서/어서: general cause → result; neutral, works with positives too.
• -기 때문에: objective, often more formal/explicit causation.
  All are grammatical here, but -느라 best conveys the busy/excuse nuance.

늦게 is the adverb form (late‑ly) modifying a verb: 늦게 오다.
늦은 is the attributive adjective used before nouns: 늦은 시간에 왔어 (came at a late hour).