I don’t know for a fact, but a screwdriver might not be hard enough. I use an old engine valve. And you can feel and see the burr after I am done.  If you have deeply grooved your water stone, you might just be out of luck. Water stones are very soft and easily damaged. I’m not overly fond of them. I use an old fashioned oil stone, much more forgiving.

Waterstones require re-flatening frequently anyway with diamond stones or sandpaper on a glass or granite plate, or something similar. You can do that to get rid of the scratch marks.   

   I too followed the online advice of polishing both sides of a new scraper with little benefit, as far as I'm concerned.  Whenever I want to restore the edges I clamp the scraper into a benchvice and carefully run a fine or medium file across the edge 2-3 times.  Then I pull a screwdriver shaft across one side at a 30-40 degree angle twice.  Turn the scraper around a repeat on the other side of the edge.  I'm satisfied with the outcome, your milage may vary.  Dave

   I too followed the online advice of polishing both sides of a new scraper with little benefit, as far as I'm concerned.  Whenever I want to restore the edges I clamp the scraper into a benchvice and carefully run a fine or medium file across the edge 2-3 times.  Then I pull a screwdriver shaft across one side at a 30-40 degree angle twice.  Turn the scraper around a repeat on the other side of the edge.  I'm satisfied with the outcome, your milage may vary.  Dave

A double-cut mill file is all you need to prepare a cabinet craper for the final burr-forming. The burr does the cutting and when renewing it is appropriate just pass the file over each face to remove the old burr.

Google <draw filing> for hints on the proper technique for squaring up a scraper's edge before forming the burr. You don't push a file across the edge, you pull the file along the edge while the file is held perpendicular to the scraper, a hand on each side. This gives you control of the squareness of the edge itself, harder to control when pushing the file....

FInd the hardest steel you have in your kit for pulling the burr. If I can't find my burnisher I use a socket wrench extension, the larger the diameter the better. Method is the same as for draw-filing: pull the burnisher toward you with the squared-up scraper held edge-up in a vise or Jorgensen screw clamp. Work the edge three or four times with your tool-of-choice being pulled toward you, changing the angle (lower the hand on the side you're forming the burr) with each successive stroke until you can a the burr being formed.

LESS IS MORE when you can feel the burr! Stop and try out how it works on a scrap piece of suitable wood.

Some prefer pulling a scraper, others push it. I do both, depending on the task at hand. In either case the scraper's held with the top edge slightly toward (or away) from you, your hands placed so you can warp the scraper to make the burred edge very slightly curved, putting that burr you carefully formed against the workpiece you want it to cut into. Push or pull without bearing down against the workpiece, use your sense of how it's working to decide whether to push a little more firmly against the workpiece, or to put a harder burr on the scraper.

Waterstones can be quickly and easily cured of scratches or unevenness by working them over wet-or-dry sandpaper (used wet!) held flat on a plate glass or truly flat marble or granite slab.

Scrapers don't need 'polishing' on a waterstone. Working their edges is best done with double-cut mill files. Save your stones for honing your other cutting tools' final cutting edge.