Sounds like there is dirt or grit on a roller.
Examine the cross over rollers first, these are the rollers that transfer the paper from one bath to another. Ideally, they should be soaked in a water bath after use.
To find what area the scratch is happening, you should run a sheet through the machine with lights on and all crossover removed. Then you can examine the sheet as it exites the dev. If no scratch then you know it's not the dev tank rollers. Repeat with each tank.
If you find the offending set of rollers, remove them and wash and soak in water.
You could also try an old trick. Use a sheet of sandpaper, fine or very fine, and put it through the processor, the sandpaper facing the way the photo paper emulsion goes. Then dispose of the sheet of sandpaper. You may need to repeat with a fresh sheet.
This trick has worked for me in the past and was shown to me by a Fuji engineer.
Let us know how you get on.