It's not possible to modify the look of these hyperlinks in GNOME Terminal and other VTE-based terminals. At least not without modifying VTE's source, removing the loop that paints them.
I find it visually distracting
The look was chosen to be as little distracting as possible, and without conflicting with any other visual element that terminal emulation offers. E.g. the two common methods of showing them on HTML pages: modifying the color was out of question for the latter reason, and solid underlying was out of question for both of these reasons.
and pointless
I disagree with this. If these links weren't highlighted in some way, you would have basically no chance of knowing that there was some auxiliary data associated with them. You would have to crazily (or systematically) drag the mouse to discover any such text.
Of course you might be aware of a few concrete cases, e.g. that the output of ls --hyperlink
consists of such hyperlinks, but you still wouldn't recognize if an application that's brand new to you emits such links, or an app that you're already familiar with adds them as a new feature.
With no visual representation of hyperlinks, the feature would be way less useful.
(It's not like the automatic detection and linkification of http://...
-like text. There all the data is already visible, there's indeed no point in underlying. When you hover with the mouse, a solid underline lets you know that the terminal offers some convenient quick ways for some of the actions that you're likely to wish to perform on that piece of text.)