My '75, which I bought a few months ago, came with a new plastic cowling that goes above the well for the windshield wipers.  There was none in place when I got the car.

  If the piece that you are speaking of is the part I think it is, it is an after-market part that covers the area beneath the wipers.  Might check the aftermarket to see if it's still available and ask how it's attached.

Yes, thanks.  I found it at:  https://www.paragoncorvette.com/corvette_parts/instructions/8735.pdf

AFAIK this part was always an aftermarket add-on.  I think the idea was to keep leaves, etc out on that area below the wipers.

Yes, that's an aftermarket part.  Not original to the car.

I am just getting ready to paint the cowl area in my 75. Now that I have it cleaned up I like the open look which is the way they came originally, but of course remember it is what you want it to look like as you are the one driving it.

  I installed one  on my 79. I thought about double stick tape but used screws instead. I just drilled a few holes on the lip that the front of the cover sits on. I also put a little tab on the side of the fender in the well, where the wiper arms are , because the ends of the  cover didn't conform to the curve of the windshield. They stuck up a little bit. I was able to also screw the ends down and you don't have a gap  at the end of the cover at the windshield. I also used a little weatherstrip on the sides of the cover to hide that gap. After it was done, it gives a cleaner and finished look to that area. I also painted the screw heads black to match the cover that I painted black.

The one I installed on my 74 suggested velcro tape. Works good, eliminated need to drill holes and alsdo makes it removable to clean out any junk that makes it way in there.