Google Talk Chatback Badge does not work in Google Sites, because Google Sites doesn't allow using iframe tags. The HTML source I tried using:
<IFRAME src="http://www.google.com/talk/service/badge/Show?tk=z01q6amlq2h32u2hfngeg8dbu3f9o18c3qratisn4o67sj2q8poaddi6l680miq472rs99p5ptpcl4ndiugks6j1jh96ocoakvif63trigqq4tv1m4ap0n6s59t3g1oi2rkqrfqt8a4vle23j6kf7nn80i5l6o5gjp6srpq8n&w=200&h=60" frameBorder=0 width=200 height=60 allowTransparency></IFRAME>
You can get your Google Talk Chatback Badge here (for Gmail and Google Mail users):
http://www.google.com/talk/service/badge/New