I come across many LCD's with incandescent globes inside them not LED's for the backlight, and designing the resistor for a 2.4V led will result in a whack of over-current. Just increase the series resistor to the backlight pins untill the display is only as bright as it really needs to be (try 150 ohms), this will certainly get you out of trouble with the regulator, and as they already advised you, feed it from the 'raw' side of the regulator not from the 5V regulated side. The backlight is completely isolated from the 5V rail of the LCD.