My guess is that it probably goes like this:
inspire.scot advertises for Startpage across different platforms (Facebook, Twitter, etc.) using their own URLS to redirect to Startpage. The reason they do this is to keep track of the traffic information that they are sending over to Startpage and to check to see if they are meeting their advertising goals.
I’m not sure why Startpage would need a service like this, didn’t Duckduckgo grow organically?
I found this: https://www.inspire.scot/our-services/search-engine-optimisation-packages/pay-per-click
Scrolling down a little there is a section called: " So what actually happens in a PPC campaign? When we work with Google Adwords, the basics are as follows:"
When people click on advertising links on Google (I’m also assuming Facebook, Twitter, etc), inspire.scot can see “impressions”, “display network sites that sent traffic to you”. I think that they use an inspire.scot URL to redirect people to Startpage.com in their advertisements, this allows inspire.scot to keep track of clicks, impressions, etc.