I2C Display - Write Error 33281

What error do you get when you use i2c = new I2C() instead of I2C1? And you're sure you changed all instances of I2C1 to i2c? It wouldn't be the same error message on software I2C.

Your board does have 'jumpers' on it for the I2C address, so I don't know whether the default state is all pulled up or all pulled down. Maybe you could try:

require("HD44780").connectI2C(I2C1, 0x20);

all the way from 0x20, 0x21 ... 0x27. And for some reason the example on the reference even gives 0x3F which might be worth trying - but I'm not sure where that comes from!

Also could you tell us the top line of text on the chip on the PCB? I can't make it out on the picture but if it's not PCF8574 then the address could be different.

edit: If you're using software I2C with i2c = new I2C() then input_pullup is what you'd expect. The pin state gets changed on the fly as it writes, but using the internal pullup means it doesn't need external resistors.