Hide the recaptcha field in a gravity form until the user has started entering text.

WP-gravityformshiderecaptcha.php

<?php
add_action( 'wp_footer', 'ds_gf_footer', 99);
function ds_gf_footer() {
  ?>
  <script>
  jQuery(window).load(function() {
    jQuery('.gform_wrapper').each(function(){
      var recaptcha = jQuery(this).find('.ginput_recaptcha');
      if (recaptcha) {
        recaptcha.parent().hide();        
        jQuery(this).find('input, textarea').change(function(){
          if (recaptcha.parent().css('display') == 'none')
            recaptcha.parent().fadeIn()
        })
      }
    })
  });
  </script>
  <?php
}
?>