A curious entry that is hard to explain as anything other than a misunderstanding at some level. Normally in grammatical texts pepoihme/nh fwnh/ ('constructed word') refers to an onomatopoeic word: so e.g. Etymologicum Magnum s.v. bro/mos (215.45) and r(oi=zos (705.15). A possible solution comes in a passage preserved in ps.-Theodosius, On Grammar 61.13: e)/sti de\ poia\ h( pepoihme/nh fwnh/ ("the constructed word is of a certain quality"); in the context the author goes on to define the potential qualities (specifically in the realm of accent) that the 'constructed word' can possess. It could be that the last four words of this statement (which are the same four words that constitute the current headword + gloss) were at some point abstracted from the context and misconstrued as an attempt to gloss the first word of the group.
An alternative (or perhaps complementary) explanation arises from the treatise of John Philoponus, On words that take on various meanings according to a difference of accent. At one point Philoponus distinguishes between poi=a ('of what sort?') and the present headword poia/. While the former is glossed consistently as an interrogative, the latter is glossed differently in different recensions: h( poio/ths, h( poristikh/ (recension A, pi14: "quality, the providing one"); h( poihtikh/ (recension B pi26, C pi11, D pi13: "the productive/poetical one"), and finally, in recension E pi17, the present gloss h( pepoihme/nh ("the constructed one"). This last gloss seems less pertinent than those of the other recensions, but it may be this one that was picked up by later authors.
It is also possible that at any point in the hypothetical processes described above, confusion may have entered between pepoihme/nh ('constructed') and pepoiwme/nh ('endowed with a quality').
Regardless of where it came from, the same gloss appears at Etymologicum Magnum 677.57, along with comments on accentuation that align it with the genealogy of texts like Philoponus's.