Ah. I guess it works, but I suspect it would not in ajax mode?
If you have access to the PHP template file that is the one that outputs the while loop (inside the products container), you could add some PHP and use that to include some CSS to hide the reset button, like this:
<?php
global $searchandfilter;
$sf_current_query = $searchandfilter->get(1234)->current_query();
if (!($sf_current_query->get_search_term()=="") { <?
<style>
.woof_submit_search_form_container {display: none;}
</style>
<?php } ?>
Note: you would need to change the ID number, and it looks like you don’t have a search box, so this should work.
BTW, I think you need to add style like this also (generally):
.woof_redraw_zone {display: flex;}
This will stop content from below bleeding on to the ‘menu/form’.