How to Remove Checkbox for Excerpt Under Screen Options

You can do this with CSS.

.metabox-prefs label[for="postexcerpt-hide"] { 
    display: none; 
}

In regard to adding the CSS to the admin section, you have two options:

Option 1: Add the CSS to a stylesheet and enqueue it using the admin_enqueue_scripts hook.

function load_custom_wp_admin_style() {
  wp_register_style( 'custom_wp_admin_css', get_template_directory_uri() . '/admin-style.css', false, '1.0.0' );
  wp_enqueue_style( 'custom_wp_admin_css' );
}
add_action( 'admin_enqueue_scripts', 'load_custom_wp_admin_style' );

Option 2: Add the CSS to a style tag using the admin_head hook.

function remove_post_excerpt_checkbox() {
  ?>
    <style>
      .metabox-prefs label[for="postexcerpt-hide"] { 
        display: none; 
      }
    </style>
  <?php
}
add_action( 'admin_head', 'remove_post_excerpt_checkbox' );