Sounds like there's a lot more going on in your custom template than what you've shared here.

I suspect you've got a custom html_header.php file in that same folder which is causing your problem.

The core original Zen Cart code would never generate a link like you posted (ie: template.css) since Zen Cart never calls its file:
Code:
<link rel="stylesheet" href="includes/templates/template_default/popup_shipping_estimator/template.css" type="text/css" />
So, your problem lies in whatever you've coded to specifically call template.css instead of using the normal stylesheeting support in ZC.