Only show images/attachments within the gallery?

Hey,
I have the following question: When i create a page, add a gallery, and browse this gallery on the front-end it will browse all the attachments that are associated with that page, instead of just the images within that gallery. Is there a way to filter all the other attachments and only show the images with a certain gallery? So that, for instance, when I delete the gallery and add a new gallery on the same page > only the new gallery is shown?

Any ideas?
Thanks!