Ok so I added an if statement and that works, however it only stops the display of the edit link, not the actual editing itself.
<?php
$author=get_the_author_meta( 'ID' );
$currentuser=get_current_user_id();
if ($author == $currentuser):
?>
<?php
if (! empty($_GET['gform_post_id']) )
{
// show the form
gravity_form(1);
}
else
{
// otherwise show a link to edit the form
do_action( 'gform_update_post/edit_link', 'text=Edit '. get_the_title() );
}
?>
<?php endif; ?>
I am a beginner to php, but that does seem to work for now.