Stripping out HTML from <?php the_excerpt() HELP

When I create a post with HTML code and hyperlinks they don’t show up in the category section, only the post

Don’t show up here (TEST POST)
https://hollywoodscreenwritingsecrets.com/?cat=5

but they do show up when you click on an individual post
https://hollywoodscreenwritingsecrets.com/?p=204

Any thoughts? This is driving me batty!

An example of another website I saw that is doing it link I want.

https://www.3xmethod.com/?cat=12
https://www.3xmethod.com/?p=254

I was told on another forum that it is my <?php the_excerpt()
Is there a way to NOT have the HTML & Links stripped out?

Here is my code from my Archive.php
——————————————————————-
<?php get_header(); ?>

<div id=”content”>

<div id=”contentleft”>

<div class=”postarea”>

<?php include(TEMPLATEPATH.”/breadcrumb.php”);?>

<?php if (have_posts()) : while (have_posts()) : the_post(); ?>
<h1>” rel=”bookmark”><?php the_title(); ?></h1>

<div class=”date”>

<div class=”dateleft”>
<p><span class=”time”><?php the_time(‘F j, Y’); ?></span> <?php _e(“by”, ‘studiopress’); ?> <?php the_author_posts_link(); ?>  <?php edit_post_link(__(‘(Edit)’, ‘studiopress’), ”, ”); ?>
<?php _e(“Filed under”, ‘studiopress’); ?> <?php the_category(‘, ‘) ?></p>
</div>

<div class=”dateright”>
<p><span class=”icomment”>#comments”><?php comments_number(__(‘Leave a Comment’, ‘studiopress’), __(‘1 Comment’, ‘studiopress’), __(‘% Comments’, ‘studiopress’)); ?></span></p>
</div>

</div>

<div class=”clear”></div>

<?php the_excerpt(); ?><div class=”clear”></div>

<div class=”postmeta2″>
<p><span class=”tags”><?php _e(“Tags”, ‘studiopress’); ?>: <?php the_tags(”) ?></span></p>
</div>

<?php endwhile; else: ?>

<p><?php _e(‘Sorry, no posts matched your criteria.’, ‘studiopress’); ?></p><?php endif; ?>
<p><?php posts_nav_link(‘ — ‘, __(‘« Previous Page’, ‘studiopress’), __(‘Next Page »’, ‘studiopress’)); ?></p>

</div>

</div>

<?php include(TEMPLATEPATH.”/sidebar.php”);?>

</div>

<?php // The main column ends ?>

<?php get_footer(); ?>