It's not sufficient solution, spam bots already know links so hiding them will not help you.
Here is your code:
<?php if (osc_is_web_user_logged_in()) : ?>
<div class="report-wrap" style="display:none;">
<div class="head"><?php _e('Report listing', 'zeta'); ?></div>
<div class="wrap">
<div class="line"><?php _e('If you find this listing as inappropriate, offensive, or spammy, please let us know about it.', 'zeta'); ?></div>
<div class="line"><strong><?php _e('Select one of the following reasons:', 'zeta'); ?></strong></div>
<div class="text">
<a href="<?php echo osc_item_link_spam(); ?>" rel="nofollow" class="btn btn-white"><?php _e('Spam', 'zeta'); ?></a>
<a href="<?php echo osc_item_link_bad_category(); ?>" rel="nofollow" class="btn btn-white"><?php _e('Misclassified', 'zeta'); ?></a>
<a href="<?php echo osc_item_link_repeated(); ?>" rel="nofollow" class="btn btn-white"><?php _e('Duplicated', 'zeta'); ?></a>
<a href="<?php echo osc_item_link_expired(); ?>" rel="nofollow" class="btn btn-white"><?php _e('Expired', 'zeta'); ?></a>
<a href="<?php echo osc_item_link_offensive(); ?>" rel="nofollow" class="btn btn-white"><?php _e('Offensive', 'zeta'); ?></a>
</div>
<div class="line center"><?php _e('Thanks for helping us!', 'zeta'); ?></div>
</div>
</div>
<?php else : ?>
<div class="report-wrap" style="display:none;">
<div class="head"><?php _e('Report listing', 'zeta'); ?></div>
<div class="wrap">
<div class="line"><?php _e('Please log in to report this listing.', 'zeta'); ?></div>
<div class="text center">
<a href="<?php echo osc_user_login_url(); ?>" class="btn btn-primary"><?php _e('Login', 'zeta'); ?></a>
</div>
</div>
</div>
<?php endif; ?>
<script>
document.querySelector('.report-button').addEventListener('click', function(e) {
e.preventDefault();
document.querySelector('.report-wrap').classList.toggle('visible');
});
document.addEventListener("DOMContentLoaded", function() {
document.querySelector('.report-wrap').style.display = 'none';
});
</script>