Hello,
My apologies, the animation is a GIF so there is no control bar. Let me try to clarify.
If you have uploaded the media to a specific post or page, then there will be an attachment URL for your media that is related to that post or page.
However, if you visit your Media -> Library menu, and locate the media, clicking on it will bring you to the Attachment Details screen, where you can copy the permalink for the file.
Additionally, in your Customize -> Background menu, you should also be able to locate any media that you’ve uploaded, regardless of which post you attached it to.
I hope this helps!