Clearing display of lcd
Summary

You can probably separate the standard parallel LCD from the serial board and use the parallel display directly.

Serial display

The E-Term looks like the display section (top board) has a 16-pin parallel 4x20 character LCD on a board which is attached by a 16-pin connector and standoffs to a parallel to serial adapter (part of bottom board).



If you have no software information on the serial-adapter command-interface, it will be very difficult to use.

Better documented displays

That vendor offers other displays which have much more documentation. Including 
example Arduino sketches. 

You could try these and see if your display interface uses the same or a similar system of commands (using STX and ETX characters to bracket commands within displayable data).

This may end up being a frustrating dead end.

Parallel display portion

There is a good chance the top board uses a standard 16-pin parallel controller and if so, it can be detached from the other board and can be driven using the Arduino LiquidCrystal library.

This library has many functions including ...


clear the display - clear()
position the cursor - setCursor(column, row)
move cursor to top left - home()


Since there are numerous tutorials for this and huge numbers of people using it, you may find this an easier path.

It does use six GPIO pins instead of two. You probably are not (yet) short of GPIO pins on your Arduino clone.

Note that a regular Arduino's A0-A5 (or more) pins can also be used a digital IO pins.

Arduino Megas (and similar clones) have many more GPIO pins which can also be used (so long as you load the relevant "core" into the IDE and then select the right board in the IDE)

Personally, I'd expect this to be the easiest way forward.  



Example

This is an old Arduino Duemilanove - it has limited GPIO pins. However it is driving a MIDI shield which has two MIDI ports, 3 pushbuttons and 2 analog potentiometers. 

I had no problems finding 6 GPIO pins (plus power and gnd) to connect up a parallel LCD. 4 data (yellow). enable (yellow) RS (blue). Your Arduino-clone has far more GPIO than this and so you shouldn't have much problem.

The mini breadboard is there to make the connections easy and to provide LCD contrast control by potentiometer.