"우리가 모르는 척 업무를 볼 수는 없지 않습니까?"
Could you tell me what does it mean? Does it mean "We can't see that you are not working?" (You're just pretending to work, not really working)
To be honest, I'm really confused with "모르는 척 업무". What does this mean?
*I know what -ㄴ/은/는 척 하다 means
We Korean people used to omitting words whatever. In this case, you can consider it as following.
우리가 (그것을) 모르는 척(하고), 업무를 볼 수는 없지 않습니까?
우리가 (그것을) 모르는 척(하며), 업무를 불 수는 없지 않습니까?
This sentence is a rhetorical question, that is an ironical expression, so the meaning is "We are not able to work as if we didn't know of it".
We Korean people like the humor and satire, so there are a lot of expressions such as that, in Korean.
수사의문문(修辭疑問文) or 반어의문문(反語疑問文)