Twitter widget that hides links to own site

I’m using a Twitter widget (came with the theme) to display my latest tweets.
I’m also using a plugin to push my new posts to Twitter.

So when I publish a new post I will have the link to the post at the top – and right beside I will have the Twitter widget linking to the exact same post.

So I’m wondering if there is a way to hide tweets linking to my site from the widget? Will change to another Twitter widget it necessary.