Using specific image classes in posts

My ‘client’ (well, a family member) wants to be able to add a sort of border picture to her posts, individually. I have created a class for it. Problem is, the image is displaying in the snippet for the post as well, and obviously it’s made for the full length post, so it looks wrong. I’m almost certain that images aren’t supposed to display in post snippets other than the featured image, so suspect this is because I’m using my own image class. How does WordPress prevent post images from being shown in excerpts?

Thanks for any help anyone can provide.