Learn Hardcore Korean: tapseunggwoneul ilheobeorimyeon hanggongsa kaunteo-eseo dasi balgeupbadaya haeyo. - If you lose your boarding pass, you have to get it reissued at the airline counter.

을 is the object particle. It marks 탑승권 as the direct object of the verb 잃어버리면 (if you lose). In English you’d say “lose your boarding pass” where your boarding pass is the thing being lost.

What’s the difference between 잃다 and 잃어버리다, and why is 잃어버리면 used here?

잃다 simply means “to lose.”
잃어버리다 is a compound verb (잃다
- 버리다) that emphasizes fully losing something or doing it unintentionally.
  In everyday speech Koreans almost always use 잃어버리다 when talking about losing items. The -면 ending makes it “if/when you lose.”

What function does -면 serve in 잃어버리면?

-면 is a conditional ending meaning “if” or “when.” So 잃어버리면 means “if (you) lose (it)” or “when (you) lose (it).”

Why is 에서 used in 항공사 카운터에서 rather than 에?

에서 marks the location where an action takes place. Here, 발급받다 (to receive reissuance) happens at the airline counter.
If you used 에, it would simply mark a destination or existence (“to” or “at” in a static sense) rather than the site of an action.

Can you break down 다시 발급받아야 해요?

다시: again
발급받다: to receive an issuance (발급 = issuance, 받다 = to receive)
-아야 해요: indicates obligation or necessity (“must”)
Put together: “You must get it reissued again.”

Why not just say 발급해요 or 발급받아요?

발급해요 would mean “I issue (something)” – the airline does the issuing, not you.
발급받아요 means “I receive an issuance,” which is grammatical, but lacks the necessity nuance.
발급받아야 해요 explicitly means “you have to receive reissuance.”

What exactly does -아야 해요 express, and how is it different from -아야 돼요?

Both -아야 해요 and -아야 돼요 express necessity (“must do”). There’s no real difference in meaning; -아야 해요 uses the verb 하다, while -아야 돼요 uses 되다.
Example:

가야 해요 = I have to go.
가야 돼요 = I have to go.

Is 카운터 a Korean word? What does it refer to?

카운터 is a loanword from English counter. In the airport context, it refers to the airline’s check-in or service counter where you show documents and receive boarding passes.

Could I say 체크인 카운터에서 instead of 항공사 카운터에서?

Yes. 체크인 카운터 (check-in counter) is equally common and more specific.

항공사 카운터 emphasizes that it’s the airline’s desk.
체크인 카운터 focuses on the check-in function, though it’s usually run by the airline as well.