Feb 03, 2015 09:17 PM|Zhi Lv - MSFT|LINK
As Careed said, you didn't actually delete the cookie. As for delete a Cookie, we could set the cookie's expiration date to a time in the past. Like this:
If (Not Request.Cookies("UserSettings") Is Nothing) Then
Dim myCookie As HttpCookie
myCookie = New HttpCookie("UserSettings")
myCookie.Expires = DateTime.Now.AddDays(-1D)
For more details, please refer to this articles.