Измените +=
на =
. Он будет отменен последним нажатием кнопки.
private void F1_UpdateEventHandler(object sender, Form1.UpdateEventArgs args)
{
label1.Text = "NAME : " + args.txt1Data + Environment.NewLine;
label2.Text = "EMAIL : " + args.txt2Data + Environment.NewLine;
label3.Text = "SSC : " + args.txt3Data + Environment.NewLine;
label4.Text = "HSC: " + args.txt4Data + Environment.NewLine;
}