Your minified stylesheet main.min.css contains this:
a{color:#000;text-decoration:none;border-bottom:1px dashed #000}a:hover{border-bottom:1px solid #000}
It looks like this is causing the issue you describe. I didn’t see these rules in the unminified version you posted.
You need to change this so that the border is not applied to all links by specifically targeting the elements you do want it to be applied to.
The theme is built differently from most WordPress themes in that the style.css is not used to provide styling as it would normally be.
If you post on the theme’s own support forum at https://www.ads-software.com/support/theme/underline the theme author or other users of the theme are more likely to see your question and hopefully provide you an answer based on how the theme is intended to be used.