Controlling 16x2 LCD backlight (I2C module)
It's hard to tell from the limited information, but chances are the "backlight jumper" mentioned in passing in the datasheet can be simply removed.  This will then give you two pins.  One will connect to pin 3 of the IO expander, and the other will connect to the back light anode itself.

Which is which you will have to discover for yourself.  One of them will have the 100Ω resistor in line with it as well.

If you can't see the tracks (some black boards are hard to make them out) then you should get a digital multimeter and set it to continuity mode and probe the pins to see where they lead.

Once you have identified which pin is which you can connect the one that goes to the back light to your Arduino and drive it with PWM.