My personal preference here is rewriting the query or working with a namevaluecollection at a lower point, but there are times where the business logic makes neither of those very helpful and sometimes reflection really is what you need. In those circumstances you can just turn off the readonly flag for a moment like so:
// reflect to readonly property
PropertyInfo isreadonly = typeof(System.Collections.Specialized.NameValueCollection).GetProperty("IsReadOnly", BindingFlags.Instance | BindingFlags.NonPublic);
// make collection editable
isreadonly.SetValue(this.Request.QueryString, false, null);
// remove
this.Request.QueryString.Remove("foo");
// modify
this.Request.QueryString.Set("bar", "123");
// make collection readonly again
isreadonly.SetValue(this.Request.QueryString, true, null);