I checked the Oxygen demo site, and I don't see borders around the featured post titles but I do see background colors set for the featured post titles and dates:
http://oxygendemo.wordpress.com/
To remove the backgrounds from the featured post titles and dates on the Oxygen theme showcase page, add this to your Appearance → Custom Design → CSS editor:
.featured-post .entry-title a,
.featured-post .entry-meta,
.featured-post:hover .entry-title a,
.featured-post:hover .entry-meta {
background: transparent;
}
However, I wouldn't recommend doing that because it may make the text really hard to read depending on the images you've uploaded.
For the future, would you please make sure to include a link to the blog you're working with when you ask questions in the CSS forum? Thanks!