For dye production, fully mature females are collected and dried. In the Roman empire, they were called “grana” because they resemble seeds when dried.
The word “carmine” is derived from “Kermes”. “Vermilio” refers to worm (vermes). From “vermilio” we get “vermillion”, which means red. Recently, Kermes vermilio has been a pest in Italy, with outbreak populations causing damage to oak trees* which made some people see red.
*GIUSEPPINA PELLIZZARI, FRANCESCO PORCELLI, STEFANO CONVERTINI & SALVATORE MAROTTA. 2012. Description of nymphal instars and adult female of Kermes vermilio, with a synopsis of the European and Mediterranean species. Zootaxa 3336: 36–50.