V지말아줄래? is used when speakers want listeners not to do something. For example 1. your sister is eating your food without your permission. At the moment you can use this expression. 내 음식 먹지 말아줄래? (Do not to eat my food please?) 2.You’re watching the movie in the theater but someone is standing up in front of you for long time. At this moment you can use like this. 화면을 가리지 말아 줄래요?( Would you like not to block the screen?)

Would you pls not to ~V (It's a politely asking something not to do, to your friends. Because it is 반말) V-지 말아줄래? Would you pls not to do it? 그것 하지 말아줄래?