Depends on how you are showing the Form2.
If you show it via ShowDialog, then you will have to add a return code as a property (or use the DialogResult return) which you then interrogate:
Form2 f2 = new Form2();
if (f2.ShowDialog == DialogResult.OK)
{
if (f2.UpdatedOK)
{
myButton.BackColor = Color.Green;
}
}
If you use Show instead of ShowDialog, then you need to create an event in Form2 which your first form handles. In the handler you set the colour.