Paul Oerth saw my recent article in Measurement News about what the counter looks like when disassembled. He had a problem with a counter that ran backwards. He sent it to me for dissection, to try to figure out why it ran backwards.

All it took was one look, and no taking apart. Standard JO counter on left, backwards one on right.

See the difference?
Original Post

The left one the numbers increment bottom to top the right one increments top to bottom.
If that counter is the one I think it is, check to see what the other digits are doing. Liza Recto was attempting to measure a marathon in southern Maryland. She wondered why the ones digit kept going backwards-- 0,9,8,7 etc. But once it completed a revolution, the tens digit would advance by one. I wonder if that one wheel was intended for a counter that turns the other way, or is it from a countdown timer of some sort?
My initial take on this was wrong. Examination of the wheels shows that the rightmost wheel has numbers that increase as they rise in the window. The other four wheels have numbers that decrease as they rise in the window. Somehow the factory got this one wrong. A wheel from a different model was improperly put into the counter.

Veeder-Root has a lot of models, and all are similar. They differ in which side the drive shaft is on and direction of rotation. The way the wheels are numbered depends on the model that is ordered.
A counter running backwards is no problem at all. It is the difference between two numbers that matter, not whether the second number is larger than the first.

I've seen counters put on the right side of the bike, running backwards, and the data comes out just fine.

Not a problem.