I've been able to find the solution. What we have here are two problems, first is the "Response" is a property of page and page is what we are in the script ("this" in C#). The equivalent in Visual COBOL is "self". Second, there is a problem with the Write, the double quotes do not appear to be necessary.
The following syntax does work and is your hello world for this scenario (which I could not find in the documentation):
<%@ Page Language="COBOL" Inherits="System.Web.Mvc.ViewPage" %>
<!DOCTYPE html><html>
<head runat="server">
<meta name="viewport" content="width=device-width" />
<title></title>
</head>
<body>
<%
INVOKE self::Response::Write("<h1>Hello World!</H1>")
%>
<div></div>
</body>
</html>