Learn Hardcore Korean: jeomwoni jarireul jeongrihaneura neutge wasseo. - The clerk came late because they were tidying the seats.

-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.

What exactly does -느라 mean in 정리하느라?

-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).

Is -느라고 different from -느라?

They’re functionally the same. -느라고 is the fuller form; -느라 is a common shortened form. Either is fine: 정리하느라 늦게 왔어 = 정리하느라고 늦게 왔어.

Why is it 정리하느라, not 정리했느라?

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.

Does -느라 always imply a negative or inconvenient result?

Yes, that’s the usual nuance. It’s typically used for excuses or inconveniences (being late, missing a call, not doing something). For neutral/positive results, prefer -아서/어서 or -기 때문에.

Who is doing the tidying in 자리를 정리하느라?

With -느라(고), the understood subject of both clauses is the same. Here, the clerk is both the one tidying and the one who came late: 점원이 [자리를 정리하느라] 늦게 [왔어].

What does 자리 mean here, and why is it 자리를?

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…

Could I use other words like 테이블, 치우다, 정돈하다, or 청소하다?

Yes, with slight nuance differences:

테이블을 치우느라 (clearing tables away)
테이블을 닦느라 (wiping tables)
매장을 정돈하느라 / 정리하느라 (straightening the store)
청소하느라 (cleaning)
All can replace 자리를 정리하느라 depending on the exact action.

What’s the difference between 늦게 왔어 and 늦었어?

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.

How polite is 왔어, and how do I make this more polite?

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

Can I reverse the clause order?

The cause normally comes first. Putting the result first sounds abrupt unless you add something like 그래서/그랬어:

Natural: 자리를 정리하느라 늦게 왔어.
Also okay: 늦게 왔어. 자리를 정리하느라 그랬어.

How is -느라 different from -아서/어서 and -기 때문에?

-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.

Why is it 늦게 and not 늦은?

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).

Any pronunciation tips for the sentence?

In fast speech: 왔어 sounds like [와써], and 정리하느라 flows as [정리하느라] with light liaison. The rest pronounces as written: 점원이 자리를 정리하느라 늦게 왔어.