Frontend Post Excerpt field mapping

I haven’t tried the Gravity Forms plugin but if you are using the wp_insert_post function to insert the new post, you just use ‘post_excerpt’.

example:

$new_post = array(
  'post_title'    => 'Post Title',
  'post_content'  => 'Post Content',
  'post_status'   => 'publish',
  'post_excerpt'  => $custom_excerpt_field
);

wp_insert_post($new_post);

Not sure if I completely understand your question, so I’ve misunderstood something please let me know..