There's no reason you have to get rid of them, unless you are full, there's 8 slots total, you can hold regardless of whether they're complete or not.
So you could potentially save a completed levequest for weeks on end.
The system is a bit confusing, and likely something that will be changed in the future. The exchange simply allows you to apply a bonus based on how well you did on that leve, to increase either the gil or guild mark reward of the next leve. You can apply up to 4 completed leves to 1 new leve. Or you can apply one or none to a new leve, simply press the back button (cancel) and choose exchange, without any selected, to exchange 0 leves for a new level. This will only work if there is an available slot of course, otherwise you must make at least one exchange.