Hello,
I think to achieve this, you will need to set up a full management of the signature (and redeploy them), there are such tools like Symprex, that allow you to create a signatures templates (you can also add dynamic content from AD, like phone number, name, department, etc.) and push tthe signatures to Outlook (trough an agent on computers), OWA, etc (but this require licenses).
Another possibility would be if you can find which user have the links, create a special group, and on your rule that append the links, only apply it if the user is not a member of the group, here is an example :
By the way in your scenario you should no "append" but "prepend" it, if you want it at the end.