We want these images to have alt text so they can be accessible to users with screen readers. Currently without any alt text the reader will read the URL of the image which is not so great.

For lists you may want to consider having a null alt tag alt="" so the screen reader ignores them. This is since the purpose of these list images are just as custom bullets and thus are just decoration.

However for boxes you probably want to have the image alt text as found in the image object itself.