Why do I see tweets from someone I don't follow?

[Grace]

I think she follows me, but I don't follow her, her tweets are kind of annoying too! How can I stop seeing her tweets?

[JJ]

Those are retweets.

Keep in mind:

If you see a new face in your timeline, it's because someone you follow retweeted something they thought you should see. In the message, you’ll see the picture and username of the original user, who was retweeted by someone you follow. Turn off Retweets for that person if you don’t like what they share.
Turning Retweets on or off is NOT retroactive, meaning that Retweets from someone you follow will be delivered to your home timeline while the Retweet button for them is green; Retweets will not be delivered while the button is grey.
If a particular account that you follow retweets updates that you don’t want to see in your home timeline, just visit their profile to turn off Retweets from them. Here’s how:

1. Open a user’s mini-profile by clicking their username anywhere on Twitter, or go to their full profile at http://www.twitter.com/username

2 Next to the Following button, click the Retweetsicon as shown below. Grey = OFF, so anything that person retweets won’t show up in your timeline.

3. To turn their Retweets back on, click the button to turn it green. Green = ON.