Hi,
We're talking two different things...:
1. Category listing (as per the subject of the thread)
2. Product listing (as per your post)
1. In the configuration of category listings you have the option "Show the number of products", which you can set to "No". Maybe that's what you want? As all listings, they can be configured via -> Display -> Content menus/modules.
2. Product listings, at least the classic "div" type, don't show product quantities, there's nothing in the code I can see (unless you'd mean e.g. a quantity input field or so along with the add-to-cart button). If it's different in your case: have your listing views been modified? You could see under -> Display -> Views, if e.g. "product / listing_img_title" or similar views for your template show a trash bin at the right.
If I'm completely "off" here, please show what you're referring to by a link to the shop page, or at least a screenshot, thanks.