Hi,

Don't know which decoration you mean. On my demo site the links are decorated by the template, although you can change it within the module CSS too if you like.
The links on my demo site:
a {
    color: #336699;
    text-decoration: none;
}
a:hover, a:active, a:focus {
    text-decoration: underline;
}

As for URLs from Twitter, be sure you use Twitter XML API interface, not just the RSS interface.