Remove Out of Stock image on Listing Pages

Maybe this is pretty simple but I can't figure it out. I would like the out_of_stock image to not show up on the category list pages but I do want it displayed on the actual product pages.

Can someone point me to the correct file and line to change this?

Basically, I want them to go to the actual product page before discovering that the product is out of stock.

The reason for this is because I want them to have the opportunity to sign up for email notice when the product is back in stock (very important in my business).

Here's my site if you need it: https://www.GeneralExotics.com - I have more info enabled and do not have a buy now button or add to cart button on the category listing pages.

Thank you in advance for your help!

Eric