If you cut a house and send regrets with interest, that tells the cut sorority that you may still be interested in receiving a bid from them. So, in the event that your current 3 houses do not extend you a bid, there is a possibility that you could still get one on Bid Day from the house you "regretfully" cut. It's a good method because it allows a better opportunity for girls to match with a house instead of being cut from all the houses completely.
Hope this helps a little!