The Skrreea lived in a matriarchal society, as Skrreean males were considered far too emotional to be leaders and were constantly fighting among themselves. It was not unusual for Skrreean females to have multiple spouses.
The Skrreean also had an unusual skin condition which caused them to leave flakes of skin behind. This caused those who were unused to it to treat Skrreea with disdain and believe that they were "dirty".
The Skrreean spoken language had a unique syntax and grammatical structure which caused the universal translator to struggle with it initially before it could establish a translation matrix. (DS9: "Sanctuary")
By 2370, the T-Rogorans were themselves conquered by the Dominion. The Skrreea took this opportunity to flee their homeworld in whatever ships they had, in search for the Eye of the Universe of Skrreean legend. One ship, carrying Haneek and her family, discovered the Bajoran wormhole and identified it as the Eye. Arriving at Deep Space 9, Haneek studied Bajoran history, and assumed that Bajor was Kentanna, a planet named in Skrreean legend as a "planet of sorrow" where the Skrreean people were destined to settle. Some three million Skrreean refugees subsequently arrived at Deep Space 9 in search of aid.
With no established government, the Skrreea chose Haneek as their leader. Haneek petitioned the Bajoran Provisional Government to allow her people to settle on Bajor. The Bajorans refused, insisting that they were struggling to provide for their own people's needs and could not take in three million refugees.
Haneek's teenage son, Tumak, was angered by this decision and attempted to land one of the Skrreean ships on Bajor. Unfortunately, Tumak was unaware that the Skrreean ship had suffered a high-energy radiation leak. During a short battle with the Bajoran Militia, phaser fire ignited the radiation leak and destroyed the Skrreean ship, killing Tumak.
According to Michael Westmore, the make-up designer for the Skrreea, their distinctive "bumpy skin" was created by combining little bags of pumice, found in a hobby train shop, with a liquid latex, which was then stippled onto the actors' faces and dried. (Michael Westmore's Aliens: Season Two, DS9 Season 2 DVD special features)