That is a kind of virus-like advertising program that got "snuck" onto your machine, probably when you installed another program.

I had it too and a little googling will find instructions for removal.

Here are some of the first few that appear googling "green links appearing"

Re: green text appearing on web pages are hyperlinks from ...
https://www.google.com/search?q=green+links+appearing&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a&channel=sb

Advisory: How to Remove Unwanted Text-Enhance Links from Your Website
In most cases, browser extensions are responsible for unsolicited advertisements
http://news.softpedia.com/news/Advisory-How-to-Remove-Unwanted-Text-Enhance-Links-from-Your-Website-303566.shtml

Alter the search terms a bit to find more instructions.

Sometimes the culprit is a browser extension but there can also be a program (look in add/remove programs) which makes them come back again.

One must be careful when installing programs because many installers add "free" "bonus" things like this. Just say "NO" to these which means you have to read carefully at each step of the install process. It's easy to click "Yes" by mistake.

This one goes by a number of names so the first solution you find might not work. Keep googling and trying until you find the particular one (name of extension or program) that you have.

First step: turn OFF all extensions and add-ons in the browser and see if they disappear. If they do, enable them back ONE BY ONE to find out which one is doing it.

Even when you do that there is probably an unwanted program that turns them back on. This too can go by different names so you need to search forums etc. to find all different names this program might have.

I know, it is very annoying. But you CAN get rid of this thing.