I don't know anything about the Iris brand, but I have saved a few pics of Iris saddles that were for sale on Ebay. The stamps on the side appear to say GRAN SPORT, sometimes with the letters B17 above them. Sometimes the area where B17 is expected.
A lot of Italian saddles were marked B17, surely just a coincidence, they are not really up to Brooks B17 quality. I have also seen A17 saddles.
I have also seen a lot of saddles with this exact frame and hardware on eBay with different badges and different stamps. The white plastic layer under the leather is distinctive, so I'm pretty sure they are from the same factory. Often the stamps say GLR, NUOVA PRODUZIONE, and BREVETTATA. The badges often say S. MARCO but I have seen other brand names, such as GARLATTI.
I don't know who made them, but the S. Marco badge seems to be a hint.
Sometimes they are leather, sometimes they are black nylon, apparently shaped in the press made for shaping leather. They nylon ones are hard as rock, do not look comfortable.
The most interesting thing is these 1970's Italian saddles use pre-1950 Brooks nose hardware, or at least an exact copy. Brooks changed their nose hardware in 1950, when they introduced their current nose hardware. The older stuff was more expensive to produce, so the 'new and improved' model was mainly better because it was cheaper. So it is bizarre to find the older design used on these Italian saddles-- it really looks as though they bought up a ton of Brooks nose hardware when Brooks changed the design. Which doesn't make much sense, but there it is.