LCD - 2 Different Circuits

Does anyone know if this smaller red board on the back of the LCD comes off? All over the internet I’m seeing two different ways to hook up this LCD and I can’t get it to work with this red board on the back so I’d like to try it without it.

There is no need to remove the backpack. I2c is much simpler to wire up than when using arduino pin control.
Also, without the proper de-soldering tools the device can be damaged when attempting to remove the backpack.
All you need is the proper library.
With the right library it can actually be much simpler to use as well.
I would suggest that you use my hd44780 library package.
Unlike other libraries, the hd44780 library can autodetect everything for that backpack device.
It is also faster and has additional capabilities over other libraries.
I have that exact same backpack and have tested it with the library.
hd44780 can be quickly and easily installed using the IDE library manager.
You can read more about it here: GitHub - duinoWitchery/hd44780: Extensible hd44780 LCD library
The git repo page includes information about the library including how to install the library.
I would highly recommend that you use the IDE library manager and not attempt to install it manually or using the zip install.
The i/o class you will use for that device with the backpack is hd44780_I2Cexp.
The library comes with a diagnostic tool (I2CexpDiag) which will test your i2c signals and the internal memory of the LCD module. Run that first to verify that library is able to communicate with the device.

I recommend that you read through the information on the git hub repo before you go off trying too run the examples. There is also information about the examples down under the examples directory that you can view on the github page.
The examples for that device will be the ones under the hd44780_I2Cexp i/o class area.

--- bill