옛날에는 아이를 입양한 부모들이 누가 그 사실을 알기라도 하면 큰일이라고 생각해서 비밀로 했는데 말이야.
=> You know, in the old days, parents adopting a child used to keep it secret thinking it was a big deal if others knew about it.
* VERB-기라도 하면 is an emphasized form of VERB-면 - it implies the action or event is an unusual or dreaded one.
-면 = if you VERB;
-기라도 하면 = if you so much as VERB; if you by chance happen to VERB.
- 지진(이) 나면 어쩌려고 이렇게 허술하게 지었나? if earthquake happens.
- 지진이라도 나면 어쩌려고 이렇게 허술하게 지었나? if something like earthquake should happen.
* -는데 말이야 has the nuance of "I'm saying", "what I mean is", "you know", etc. It is usually a filler that indicates what's said is familiar to the speaker. It also adds an informal and familiar feel to the sentence.
- (watching a game) 왜 저렇게 못할까? 내가 하면 잘할 것 같은데 말이야.
- 바로 거기가 좀 이상하네. 다른 건 다 좋은데 말이야 (It's a bit weird right there. Everything else is pretty good, though).