You may notice that some features on Blogger do not display a featured image for a post. This is usually caused when the images in your posts are hosted externally from Blogger. For example, the images in a post might be hosted on Flickr or Photobucket.
Blogger will only display images in a grid layout or the Popular Posts widget if it has been uploaded directly to the post content. This is a Blogger system restriction which we cannot change via the template, unfortunately.
We generally recommend that you upload all images directly to Blogger rather than hosting them externally. If this is not an option for you, then you can work around this by adding at least one image to the post that has been uploaded to Blogger. If Blogger is able to find one image within the post, it will use it, even if the remaining images are hosted externally.
Note: this is unrelated to another issue with Blogger and missing posts on the homepage. You can read about this in this article.