Like ataradov says, the backlight is separate. In the picture you linked, R8 is a current limiting resistor, but it may be a 0 ohm resistor or a very low value by default, so it would allow too much current to go through the backlight.
You can add a resistor in series, on either the anode pin or the cathode pin, doesn't really matter which one as long as there's a resistor in series.
You have the formula V=I/R so ... the resistance value is basically [Input voltage - Forward voltage of led(s) ] = I * R .... with a 3.2v led and 5v input and 20mA (0.02A) ....you have R = (5-3.2) / 0.02 = 1.8 / 0.02 = 90 ohm, so a 100 ohm resistor would be good enough, or a 82 ohm resistor would also work if there's already another small resistor on the back of that display.
You could also have a 47 ohm resistor in series with a 100 ohm trimpot (tiny potentiometer) which would allow you to adjust "brightness" between 47 ohm and 147 ohm, so you have super bright or dimmer. Values are random, you can pick whatever values you want.