The speaker maybe a middle/high schooler. They have to hand in their cell phones to their teachers in the morning, and receive them in the afternoon/evening. 한국에서는 in Korea 휴대폰 걷는데 (people/teachers) gather cell phones ~데 means but here. 너희는 (for) you 안내도돼 is it okay not to hand in (it)? In Korean teachers gather cell phones, but is it okay for you not to hand in it?

걷다 is a contracted form of 거두다 거두다 means "gather, collect, harvest" 휴대폰을 걷다 literally means "collect cellphones" 내다 means "submit, hand in" 휴대폰을 내다 means "hand in cellphones" 한국에서는 휴대폰 걷는데 너희는 안 내도 돼? In Korea, we have to hand in our cellphones (before class starts). How about you?