Esben,
I definitely see the issue here. Tweet Blender by default is not pulling retweets and there is a checkbox under WP Admin > Settings > Tweet Blender > Filters tab that allows you to limit the stream to only original tweets.

However, by the look of these tweets it might happen that these are indeed original tweets from each user i.e. they didn't do a classic retweet (which would show a picture with a joint icon and typically include "RT" in the body of the message). So for this situation, there is easy way to filter the stream as all of these match your search query.

I might create a new filter that allows to filter out tweets that have the same content even if they come from different users. Seems like that would be a good way to deal with your issue.