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?