De Breteuil coat of arms
The idea here is that the name Brettle comes from de Breteuil, a commune in the Oise region of Normandy where Guillaume Fitzosbern, Seneschal to the Duke of Normandy, had his castle, Chateau de Breteuil. The De Breteuil coat of arms is shown here.
You can read more about the history of the Breteuil family and their chateau here (1). Fitzosbern, who fought at the battle of Hastings, was an important and faithful supporter of William the Conqueror, so much so that when King William I returned to France in 1067 he left Guillaume, Lord of Breteuil, and his brother in charge of England in his absence. William rewarded Guillaume for his service in the conquest of England with the grant of estates in the Isle of Wight and the county of Hereford, whereby he became Earl of Hereford. If you want to get into this in more dept you can find more of the history of Guillaume, his origins and descendants here (2), here (3) , and here (4). Although Guillaume had estates in Herefordshire and Worcestershire he also had major estates in other parts of England but the name Breteuil or its variants does not seem to feature strongly in English history after Guillaume’s son, Roger de Breteuil, did not keep on good terms with William and infact took part in a revolt rebelling against William in 1075. He was then tried for treason and imprisoned for the rest of his life (see here) (5), his estates forfeited and dispersed with the earldom discontinued. His two sons, Reginald and Roger, (5) do not seem to have left much of a mark in subsequent history although Roger's kin with phonetic variants of Bretell, Bretel and Breteuil are recorded in the Domesday Book as having prominence in Herefordshire where they held manorial lordships as administrators for the Norman crown. However this does not seem to have any strong connection with where the Brettles were later concentrated, i.e. South Staffordshire and North Worcestershire: because of this I do not think that that Brettle originates simply as a developing variation of the original widely distributed, but largely disappeared, Breteuil.
(1) https://www.breteuil.fr/en/breteuil-in-the-history-of-france/ Breteuil in the History of France Château de Breteuil
(2) http://www.connectedbloodlines.com/getperson.php?personID=I11055&tree=lowell Connected Bloodlines
(3) https://en.wikipedia.org/wiki/William_FitzOsbern,_1st_Earl_of_Hereford William FitzOsbern, 1st Earl of Hereford Wikipedia
(4) http://fmg.ac/Projects/MedLands/ENGLISH%20NOBILITY%20MEDIEVAL.htm England, Medieval Nobility Foundation for Medieval Genealogy
(5) https://en.wikipedia.org/wiki/Roger_de_Breteuil,_2nd_Earl_of_Hereford Roger de Breteuil, 2nd Earl of Hereford Wikipedia
(6) https://opendomesday.org/ Open Domesday