They actually use the dirt and grass from the new hole to fill the old hole. They make special tools which will cut a perfect hole an exact depth every time. Think of it as a pipe driven into the ground. When the tool is removed, the plug of dirt with the attached grass remains in the tool. That plug is then inserted into the old hole, which is an exact fit since it was made with the same tool. You’ll see a small ring where there is no grass around the old hole for a day or two until the grass fills in the gap.

http://www.greenmediaonline.com/gr/2002/0211/Images/0211scr6.JPG

All new holes removed are used to fill in the old hole. Originally 18 holes were cut and tossed, after that new holes are cut and replaced in the previous day’s holes, usually each day.