"AMMYY scam" is a generic term for conning people into putting remote desktop software on their machines and charging them. Sometimes (apart from conning you into paying fro something you don't need) it's harmless. Other times, they take take the opportunity to install trojans, keyloggers, etc.
As you've given no details of the particular scam that you were the victim of, it's difficult to give specific advice. For example what, exactly, is the icon that you can't remove?