That is coded into the website, so you'd have to inject some Javascript into the page to override the prompt.
Be careful with this, though. This requires overriding the entire window.onbeforeunload event handler, and some pages might have decided to do more than just display a prompt (perhaps save data or something similar).
To start with add a reference to mshtml, this is required to be able to set the contents of a script element (credit to Atanas Korchev):
- Right-click your project in the - Solution Explorerand press- Add Reference....
 
- Select the - Browsetab and navigate to- C:\Windows\System32
 
- Select - mshtml.tlband press OK.
 
- In the - Solution Explorer, expand the- Referencesnode. If you can't expand it or if it doesn't exist, press the- Show All Filesbutton in the top of the- Solution Explorer.
 
- Select the - mshtmlreference, go to the- Property Windowand make sure- Embed Interop Typesis set to- True.
 
Now you can use this code:
Private Sub RemoveOnBeforeUnloadPrompt()
    If WebBrowser1.Document IsNot Nothing AndAlso WebBrowser1.Document.Body IsNot Nothing Then
        'Create a <script> tag.
        Dim ScriptElement As HtmlElement = WebBrowser1.Document.CreateElement("script")
        ScriptElement.SetAttribute("type", "text/javascript")
        'Insert code to override the window.onbeforeunload event handler.
        CType(ScriptElement.DomElement, mshtml.IHTMLScriptElement).text = "function __removeOnBeforeUnload() { window.onbeforeunload = function() {}; }"
        'Append script to the web page.
        WebBrowser1.Document.Body.AppendChild(ScriptElement)
        'Run the script.
        WebBrowser1.Document.InvokeScript("__removeOnBeforeUnload")
    End If
End Sub
Then, before you navigate to a new page call:
RemoveOnBeforeUnloadPrompt()