I have been using a very stiff "knuckle" brush sold at KM and WM for many years now and it will take most marks from the edges of other matboards out and renew the knap on the texture of the suede. If you rub the board in circular motions it will tend to duplicate the original pattern of the knap better than rubbing it in a straight line.
I have a personal aversion to applying any moisture to matboards, just one of my little foibles in working with anything glued to anythin else. If steaming works for you, go for it. I find that mechanical brushing will provide the same result and it won't affect the quality of the mat at all.
All of those suggestions work, and here's one more:
If you have an air compressor, spritz a bit of clean water on the suede's marks and then blast it dry with a stream of high-pressure air. That evaporates the moisture & restores the swirl marks nicely. And you won't have to heat up your steam iron.