Strip image caption along with image

I'm using ckeditor with the image2 plugin that allows you to add a caption to an image. When I apply smart trim and ask it to strip HTML, it succesfully removes the image, but not the caption text. I would imagine that users will generally want to strip the caption along with the image.

I'd like to help with this if you think it is would be useful. I can see two ways of doing it. One is to strip captions automatically, which will keep the nice clean interface and is probably what almost all users will want, but is slightly restrictive. The other is to provide a checkbox under "Strip HTML" giving them the option to strip or keep image captions.