Removing Fields From the Profile Page of Theme My Login Plugin

From the link I provided in the comments:

All of the templates located within
/wp-content/plugins/theme-my-login/templates are easily customizable.
Just simply pick any template you wish to edit, copy it to your
current theme’s directory and edit it as you wish. Theme My Login will
always look for templates in your current theme’s directory first,
before loading it’s own templates.

So:

• create a Page Template using the file page.php of your theme as model and put a template header

<?php
/*
Template Name: Profile Page
*/

• copy all the code from /wp-content/plugins/theme-my-login/templates/profile-form.php
• paste it in your new template, substituting the loop block:

<?php while ( have_posts() ) : the_post(); ?>
  <?php /* code code code */ ?>
<?php endwhile; // end of the loop. ?>

• now you can customize everything you need