>What I did is, after selecting No Action in Avast, I opened the email message. Avast gave me a warning again but let me open the email. In the email there was a copy of the malicious script that the hosting provider found in the index page of my site. I am impressed that Avast checked for it and warned me. I am surprised that the AV software of the tech support guy of the hosting company that sent me the message didn't warn him; or maybe it did.
>
>Anyway, I downloaded the page and cleaned up the malicious script. Now I submitted a request to Google for reconsideration of my site; so they would remove the warning of harmful software. We will see how it goes.

How the malicious script got into your page?