"-(으)ㄴ데" lays down background before the main point: it softens, contrasts, or explains. Here it keeps landing on 먹다 "eat, drink". It prefaces a polite request or offer — this is a bit pricey, can I drink it? this one's already peeled, is it okay to eat? — and it gives a reason: we'll be walking a lot, so eat. It is the ending that makes a blunt question sound considerate; without it, 이거 먹어도 돼요 lands bare.