The backpack has a 2-pin header with a jumper.
Remove the jumper. Measure the current with a DMM.
Normally a 16x2 backlight would take 20mA - 50mA. Anything more and it means the backlight needs a series resistor. Some modules just have 0R resistors mounted on the pcb.
Either replace the 0R with a sensible value SMD resistor e.g. 47R
Or connect a wire-ended resistor across the 2-pin header.
David.