How to delete specific element when it is not homepage?

If I’m understanding correctly, and the code you posted is the full contents of your post, one option would be to only keep the paragraph in the main content, and add the link as custom postmeta. You would then create a child theme and edit whichever places you want links – front-page.php for the homepage, archive.php or category.php for the category, etc. – and have that pull the link from postmeta.

To add the custom field without any plugins, in the editing screen, use the “Screen Options” at the top to make sure “Custom Fields” is showing. Scroll down to Custom Fields, add the link as a custom field – perhaps link-credit or something a bit less generic than just link – and then in your template, say front-page.php:

Replace the loop containing this type of post with something like this:

<?php
// get the link-credit custom postmeta - 'true' ensures only 1 is returned
$link-credit = get_post_meta(get_the_ID(), 'link-credit', true);
if(!empty($link-credit)) {
    // display the link
    echo '<a href="' . $link-credit . '">';
    // display the content - the paragraph
    the_content();
    // close the link
    echo '</a>';
} else {
    // link to the post itself
    echo '<a href="' . the_permalink() . '">';
    // display the excerpt
    the_excerpt();
    // close the link
    echo '</a>';
}
?>

Your particular theme will determine which files, and which locations, you need to edit – and whether to use the_content() or the_excerpt().