The damper cover plate/spring is actually at 90 degrees to the pinion (input) shaft. You'll need to remove the rack to get access (which is why changing the rack makes sense, really).
If you do take the rack apart, there's a plastic bush in the long end of the housing (furthest away from the pinion shaft). That should probably be replaced. To do that, you have to unscrew the rack-end balljoint - which is round, so difficult to get a grip on.
The rack damper is a spring-loaded 'slider' that is pressed against the rack. There are shims under the diamond-shaped cover plate (underneath the rack). You may be able to get away with removing one thin shim (sometimes, there is a thick shim and a thin shim, other times, two thin shims). But, make sure the rack is not stiff to operate.
For better information, see if you can track down a Haynes manual for the 70's FIATs such as the FIAT 128 or possibly 127. They have detail on how to adjust and overhaul the steering rack.
-Alex