Trouble wiring a GDM1601 LCD to Teensy
That's a bad assumption.  Just cause it's 16 pins doesn't mean it's a HD44780 display. Of course, this one is, but that's not a good assumption to make. The datagram says:


  Built-in controller (KS0066U or Equivalent)


That's basically the same as HD44780.

The contrast pin should be tied to ground. The guide has it tied to ground. The pins on the guide are left to right. Instead, follow the pin out on the data sheet.  Don't assume your lcd has the same pinout as the guide.