Here is a photo of the mechanism in question:
What the screw does on the *other* side of the chassis is to pull a piece of spring steel (or release it) to vary the amount of tension on the treadle. The piece held and adjusted by the screw sits on a pivot that you show in your picture. Adjusting the screw to pull that piece towards
the screw means the other end, sitting on the other side of the pivot, will now push up
against the underside of the axle. The harder it pushes against the axle, the stiffer the pedal becomes.
Why does it need to do this?
Easy. Because the axle is so much closer to one end of the treadle than the other, if there was no tension, the front would always go down the moment you took your foot off of it. So, if you think of the pedal as a kind of see-saw, the front of the treadle is the 250lb cousin sitting on one end, and the pack of the pedal is the 50lb six year-old. The tension bar is the parent pulling down on the side where the six year-old is sitting, just to make things a little more even.