Per the wiki:

Tarlis Barrier Cells: Ship Enhancement:
Remnants of the original Tarlis barrier shield. Increases max shield by 15. Note: 20 are available per player.

How are there 20 available per player?

One completion of the mission (The Inside Job) gains you one Tarlis Code and one Tarlis Command Ship appears on your battle tab. On defeat of the Command Ship you get one Tarlis Barrier Cell.

75 shield vs. 300 shield. All I can think of is, you don't use the code on the ship and defeat it manually and it gives you extra cells? Or it's a typo?

Just curious. Thanks for any help.

http://galaxylegion.com/wiki/index.php/The_Inside_Job

i assumed that this note was correct:

Note: The Tarlis Code is an artifact reward from completing the mission which you can use against the Tarlis Command Ship. The Tarlis Command Ship drops another artifact - Tarlis Barrier Cells

and i updated the rest of the page accordingly.

i think what he means is how come when 1 completion = 1 tarlis command ship = 1 tarlis barrier cell, and max is 5 completions (= 5 tarlis barrier cell), but in the artifact page the note say that 20 is available per player ?

Do 1 tarlis command ship drops 4 cells ?

well, i will have to defer to someone who has actually completed the mission to make any further corrections ...

Lol no, the Tarlis ship drops 1 cell. So 5 are avaible.

I've recently started that chain:

Tarlis Barrier Cells (Uses Left: 5)

Haven't used any.