How to check in website/url have been updated or not

Unfortunately there is little you can do. I think you have the answers on your last paragraph. As far as making claims on your web site about other sources - put an app signature on your site, explain than some "less than desirable" sites are listing your apps and it should only be downloaded from <here> or <here>. Do not name or provide any information about those sites - it opens you up for legal action (and raises their profile in Google). Most savy users will track the original source down. There is little you can do about others. Also be aware that 'your' app on their sites is probably your app plus extras - hence the need for a signature.

A .Net handler can't be used with ASP because IIS can only hand the request off to one handler for each request. ASP and .Net have distinct handlers.

If you wanted to write a .Net HTTPModule to act as a Man in the Middle, the handler for the request would need to be .Net.

I've not tried it, but I reckon if you then wrote a .Net HTTPHandler to service the ASP page (which basically just runs the ASP as a VBScript), you'd have complications with the Request and Response objects. Probably more effort than its worth even trying.

An ISAPI Filter would be the most straight-forward way to go but may not be practical if you don't have the C++ experience. But what you're doing doesn't sound like particularly new ground and there may be an existing implementation you can use.