What is being underlined there is not "text" but a "link", so yeah, links are usually underlined to make them more visible.
You could try adding the CSS class ipsType_noUnderline to your A element in that code, but from what I see looking at it it seems that some of the links are added by the Javascript running. Depending on the final HTML added by the JS you should be able to add some custom CSS rule in the custom.css file.
That said, as @Marc Stridgen pointed out above, this is not something IPS can help with since it's a customization based on your usage.