Disney has different policies regarding refunds depending on your booking type.
If you are booked as a 'Room Only' with no tickets or dining plan, you are given the option to have refunded to cc or leave as a credit on your account for charges during your stay. Most people opt for the refund.
If you are booked as a "package" with tickets or dining plan, all refunds will go back to the original form of payment. So if yo pay with a gift card, I would recommend hanging on to them and labeling them 'used'. Disney can reissue and send out new gift cards, but it's a lengthy process and you have to wait for them to arrive in the mail.
If you want your funds back quickly and you paid with a giftcard .. hang on to those used gift cards!