The best I can think of is using the IsPostback property to check that.
if (!this.IsPostback)
{
    // first try
   if (Request.QueryString["save"] != null)
   {noDataFound.InnerHtml = "operation success";}
}
NOTE: IsPostback is not set on refresh, only if clicking a button or something alike triggers the ASP.NET postback action.
The other thing you could do is set a Session variable then the 'operation succesful' must be shown (probably you determine this in another Page.
// other page
Session["showSaveMessage"] = true;
// this page
if (Session["showSaveMessage"] == true)
{
    // show message
    Session["showSaveMessage"] = false;
}
A third option is to move this client side. Create a javascript action on load of the page. When a specific part is added to the query string (#showmessage), you can catch that and show the message (How to get the value from the GET parameters?).
Then redirect to the parameterless version (#) by setting the url to the stripped version. Set window.location.href or window.location.search for that (this won't cause a call to the webserver, since it is all client side).
This circumvents the drawbacks of the first solution, but introduces more code client side. Luckily, ASP.NET MVC has some mechanisms for this. Unfortunately ASP.NET Web Forms doesn't have those.