How to delete post thumbnails in index page? (twenty fourteen theme)

There’s at least 2 ways to do this and all changes should be made in a child theme.

Note: Use the 2nd method if using Post Formats.

1. In the content.php file around Line 14 change this line

<?php twentyfourteen_post_thumbnail(); ?>

To this:

<?php if ( ! is_home() ) twentyfourteen_post_thumbnail(); ?>

2. Or around line 172 of the twentyfourteen > inc > template-tags.php file you could add the is_home() conditional tag so its like this:

function twentyfourteen_post_thumbnail() {
    if ( post_password_required() || is_attachment() || is_home() || ! has_post_thumbnail() ) {
        return;
    }

Use conditional tags to remove the featured image from other archives

Source