Use action, filter, or hook to append HTML to WordPress plugin function

The do_action calls allow you to add an add_action that will run at that point int he code. Based on the code you provided, you can add a new row using the mpp_user_profile_form action, like:

add_action( 'mpp_user_profile_form', function( $user_id ) {
?>
<tr>
    <p class="appended-text">
        <strong>Note: optimum image size is 200 pixels wide by 200 pixels tall.<br>
        Maximum file size is 200KB.<br>
        (Your profile image may appear "squished" in this preview, but will appear normal on articles and events you post, and on your author page.)
        </strong>
    </p>
</tr>
<?php
} ); 

Otherwise you can append to #metronet-override-avatar div with javascript