"The portion of it that is θέσει grew to such an extent that all efforts to secret away the process of production in the work could not but fail" (Adorno, Theodor W. Aesthetic Theory. Edited by Gretel Adorno and Rolf Tiedemann. Translated by Robert Hullot-Kentor. London: Continuum, 2004. p. 33.)
θέσει, written on this page in an Ancient Greek alphabetic variant, is the dative of "thesis" and it has a specific meaning deriving from Plato's Cratylus. In this context, it pertains to the giving of names and to whether names should accord by nature with the thing they describe, or by artificial convention. (Liddell, Henry George, Robert Scott, and Henry Stuart Jones. A Greek-English Lexicon. Oxford: Clarendon Press, 1940.) θέσει represents the latter, while the former is described by Aristotle as φύσει (physei); by nature.
So, in this case Adorno is referring to the artifice of the artwork. The process of production (through labour) and its made-ness, referred to as θέσει in opposition to any naturalness, can no longer be hidden.
This is again referred to on page 82, in the following context: "The artwork, through and through θέσει, something human, is the plenipotentiary of φύσει, of what is not merely for the subject, of what, in Kantian terms, would be the thing itself."
Again, thanks to Yorgos Maragos for additional help.
Featured image by Пероша under a CC-BY-NC license.