Add option to strip Media module code

When I check the box for "Strip html", I'm seeing some output from one of my videos inserted using the Media and media_youtube module.

Here is a sample of what is displayed in the teaser:
This is some test content. This is some test content. Video of Cat Man Do - Simon's Cat Here is a test Here is another list item Here is another list item Design to theme Here is some highlighted text This is a paragraph that flows around an image. This is a paragraph that...

The media module inserts code like:
<p>[[{"fid":"110","view_mode":"4_x_3_video","type":"media","attributes":{"height":360,"width":480,"alt":"Cat Man Do - Simon's Cat","class":"media-element file-4-x-3-video"}}]]</p>

Notice the "Video of Cat Man Do - Simon's Cat?" I would think that whole phrase should be stripped out since it is just a youtube video that was inserted using the media module.

Any ideas on how I can fix this?