[Steven Zahm]

@ Matthew

The only way to do this will be to edit the card.php file for the template which can be found in this folder:
../wp-content/plugins/connections-gridder/

Move these lines to between lines 55 and 56.

<div class="cn-gridder-contact">

    <?php

    $number = $entry->getPhoneNumberBlock( array( 'preferred' => TRUE, 'format' => '%number%', 'return' => TRUE ) );

    if ( $number ) {

        echo $number;

    } else {

        $entry->getPhoneNumberBlock( array( 'format' => '%number%', 'limit' => 1 ) );
    }

    $email = $entry->getEmailAddressBlock( array( 'preferred' => TRUE, 'format' => '%address%', 'return' => TRUE ) );

    if ( $email ) {

        echo $email;

    } else {

        $entry->getEmailAddressBlock( array( 'format' => '%address%', 'limit' => 1 ) );
    }

    ?>

    <?php if ( $atts['show_social_media'] ) $entry->getSocialMediaBlock(); ?>

</div>

You will very likely also have to add CSS to make them show as the font size will likely default to 0.

This will not stop the panel from loading onclick however. Deleting the code for the panel in the card.php will likely stop it from showing.

None of this is tested, so you know, but should get you started.

Hope this helps!