Maytag dryer repair help?

You've eliminated your need for that old neutral to ground bridge. When you had the three prong plug system, you had one wire for each of the hot 110 phases and a neutral. In that case, the ground was tied to the neutral for the sake of having a conductor. Now that you have a for prong outlet, the extra conductor IS your ground, no longer requiring you to piggyback the ground connection onto the neutral.