I was once told by a greenkeeper that I did a good job. I did not have the usual implement, so I used a tee. Push the grass from about 1/4 inch around the entire indent toward the middle. It was NOT completely smooth, but he said the point was that it would grow back quickly and not 'brown out'.
If you pick up the middle, whare the sand has been compacted, you leave an empty space, the the grass above will brown and die. Grass will expand fast where it can if there is proper soil underneath.
This, BTW, is all second-hand. I may not have a clue ........