They are never looked at again.

I sometimes end up with two boarding passes, for instance when I print a receipt at the airport kiosk after printing my boarding pass at home. For amusement, I used to pocket the initialed boarding pass and use unmarked copy back when some airports required you to show the boarding pass when passing through the WTMD.

My guess is that putting a mark on each boarding pass is a method to make the document checker look at each boarding pass.

It's also easy enough to do that the TSA can score nearly 100% on an audit. A more difficult test, for instance verifying that the document checker matched names or looked at the destination airport, would fall short of 100%. And that would look bad in a GSA audit.