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Grabbing image assets from cms and file name changes

Hi. We have a webpage for members and each member on their own webpage shows a membership logo link like this- done in code.

This is great and we did this so that if a membership ceases we can change that image from our end. The problem we now have is that when we replace the image in the cms the file name changes rendering it useless. A strange side effect is that if we remove the image completely from the cms it still shows up with the code.
Any ideas i know other companies use this technique all the time

Here is my public share link: LINK
(how to access public share link)

I might add a bit more info. So basically when you change an image in the cms the url changes. This creates a problem for for external websites who are calling that url. Any suggestions please.