Yo lo traduciría así:

El logotipo Nxxx utiliza una técnica de serigrafía especial para crear un look desgastado.

Vamos a ver. Hace ya 28 años trabajé un año entero en serigrafía.

Siempre se "empuja" la tinta a través de una malla, donde tienes tu diseño...

Me da la impresión que lo de "push-through" es un poquito pleonástico, pues en la serigrafía siempre hay un "push-through"...

Aquí te lo explican de arriba abajo:

https://en.wikipedia.org/wiki/Screen_printing

The screen is placed atop a substrate. Ink is placed on top of the screen, and a floodbar is used to push the ink through the holes in the mesh. The operator begins with the fill bar at the rear of the screen and behind a reservoir of ink. The operator lifts the screen to prevent contact with the substrate and then using a slight amount of downward force pulls the fill bar to the front of the screen. This effectively fills the mesh openings with ink and moves the ink reservoir to the front of the screen. The operator then uses a squeegee (rubber blade) to move the mesh down to the substrate and pushes the squeegee to the rear of the screen. The ink that is in the mesh opening is pumped or squeezed by capillary action to the substrate in a controlled and prescribed amount, i.e. the wet ink deposit is proportional to the thickness of the mesh and or stencil. As the squeegee moves toward the rear of the screen the tension of the mesh pulls the mesh up away from the substrate (called snap-off) leaving the ink upon the substrate surface.

Por tanto, para simplificar, yo omitiría lo de "push-through".

El efecto de "faded" o desgastado, de hecho se consigue con el diseño que le des a la emulsión que se pone en el "stencil".

El ejemplo de "Larry Cook construction" en el enlace sería válido para tu contexto.

https://uslogo.net/screen-printing/

O donde dice:

A SINGLE PASS OF GOLD AND CREAM (WITHOUT A WHITE UNDERBASE UNDER) ALLOWS FOR THE TEXTURE OF THE TRIBLEND TO COME THROUGH. THIS IS A VERY POPULAR LOOK WITH THESE BLENDS! ADDING A DISTRESSED FILTER ON THE ARTWORK, EVEN ADDS MORE TO THE VINTAGE FEEL.

En este enlace:
http://www.theivsp.com/printing-dos-and-donts/

Espero que esto te ayude a aclarar el tema.

Saludos cordiales.

--------------------------------------------------
Note added at 44 mins (2018-11-02 00:08:34 GMT)
--------------------------------------------------

Diana da en el clavo... bueno, en la diana :-)

Aquí se explica:
http://blog.bellacanvas.com/reverse-screen-print/
push-through screen-printing technique

--------------------------------------------------
Note added at 45 mins (2018-11-02 00:09:41 GMT)
--------------------------------------------------

The Push Through Effect
The look of a reverse print is primarily determined by the characteristics of the fabric, since different fabrications take ink differently. The results will also depend on the color of the T-shirt and how much pressure you apply to the screen. For instance, if you want more ink to show through on the front, more pressure should be applied, and vise versa. On dark colored shirts, you typically will need more ink and applied pressure for the graphic to show through successfully. A push through print will actually dye the fabric the color of the ink, so no matter how many times you wash it, it will still hold an awesome vintage-look.