It sounds like you are not using a direct connection to power.
Ahh, now i got it. I thought you were just talking about the LCD not the backpack. But still, there is a 100ohm resistor on the lcd. Thats actually not enough(?)
Did some measuring and seems like the backpack has a transistor for backlight. Seems like the jumper connects the transistor base to Vcc via 4.7k resistor.. So when i remove the jumper, LCD gets no ground.
Yet its not clear how does the chip control backlight by software. Will be looking more later.