Strictly speaking, a poem is a grook when it was published by the Danish scientist and poet Piet Hein in one of his volumes of "grooks". Grooks are simply what Hein called his own poems; it is not a well-defined term that has been used to describe poems by other authors.
When you compare the examples on the Danish blog En sommerfugls selvmord , the English Wikipedia article "grook", the German Wikipedia article "Gruk" and the Danish Wikipedia article "Gruk", it becomes clear that there is no fixed length or rhyme scheme. They are witty and short, so it can be argued that they are a sort of epigrams.
I looked in vain for the term "grook" (or, in German, "Gruk") in the following reference works for literary terms:
- Knörrich, Otto: Lexikon lyrischer Formen. Second edition. Stuttgart: Kröner, 2005. ("Lexicon of lyrical forms")
- Lamping, Dieter (ed.): Handbuch der literarischen Gattungen. Stuttgart: Kröner, 2009. ("Manual of literary genres")
- Meid, Volker (ed.): Sachlexikon Literatur. München: Deutscher Taschenbuch Verlag, 1992/1993.
- von Wilpert, Gero: Sachwörterbuch der Literatur. Eighth edition. Stuttgart: Kröner, 2001.
As a poet, Piet Hein is fairly obscure. I did not find his name in the following reference works:
- Harenberg Lexikon der Weltliteratur. Autoren - Werke - Begriffe. In five volumes. Dortmund: Harenberg Lexikon Verlag, 1995.
- GEO Themenlexikon volumes 28-30: "Literatur. Schriftsteller, Werke, Epochen".
- Paul, Fritz (ed.): Grundzüge der neueren Skandinavischen Literaturen. Darmstadt: Wissenschaftliche Buchgesellschaft, 1991. (This is a history of Scandinavian literatures from the Reformation to the late 20th century.)
- Glauser, Jürg (ed.): Skandinavische Literaturgeschichte. 2nd edition. Stuttgart: J. B. Metzler, 2016. (A history of Scandinavian literatures from 800 to 2015.)
- Brøndsted, Mogens (ed.): Nordische Literaturgeschichte. Band II: Von 1860 bis zur Gegenwart. German translation. München: Wilhelm Fink, 1984. (Page 626 only mentions Hein's characterisation of modernist poetry: "If you have no ideas, write in an obscure way." (Danish: "Hvis du ingen tanker har,/ gør da ej din tale klar"))