Is anyone familiar with accessing 3rd party services?

I read this article: Velo: Accessing 3rd-Party Services with the Fetch API | Help Center | Wix.com
And really have no idea how to apply this to our situation. I need to call a 3rd party script () on our website. And change my links on our website to look like this after the website calls the script above. Link code: Book online now!

Can anyone help me with doing this please?