That won’t get rid of the old stuff though.
Select all the links you are using, then on the menu panel of the Links window:
Links > Utilities > Copy Link(s) To...
Then navigate to a folder you wish to copy them to.
And to complete the List: Rightclick on the .INDD File in Bridge "Show linked files" (My Bridge is german and it's called "Verknüpfte Dateien anzeigen") and then copy them where ever you like to.
(Btw. this is my favorite way of checking all linked images i know this can be done within InDesign but it's so easy to send the Images into Photoshop batch processing from bridge)