Safari adds links on any page
I think what Rob is getting at and what I think might be happening is that you have some malware (virus, etc) on your Mac (yes they do exist) that could be adding things to web pages.

It could be as simple as a browser extension or plug-in with some hijacking code in it, or something more system wide.

you could try resetting Safari (from the Safari menu select Reset Safari), turning off extensions (Safari menu -> preferences -> extensions. then turn them all off) or going into private browsing mode (Safari menu -> private Browsing). 

Optionally you could try another browser, Chrome or Firefox would be my choices. If they do the same thing then it may be system-wide and time for a virus checker or a visit with your favorite Mac repair shop (Apple store or local reseller) to determine what is going on.

Also some routers and some ISPs inject ads and other stuff into web pages. Try it on a different WiFi (Starbucks, etc...) and see if the issue goes away