Various etiquettes and rules for dressing came with Islam. How did the non Muslim women dress when these rules were revealed? How did the Prophet and his Companions react to them?
First of all , Islam wasn't as binary in its arrival as some people think , it took a long time for people to abandon their pre-Islamic habits , it didn't happen overnight , the female dress was one of them .
Now , there existed some references to Arab women's outfits in the pre-Islamic era which , obviously , continued to be the outfit of non-Muslims in the early Islamic era .
On a side note : Pre-Islamic Arab outfits were basically different forms of long dresses , so it wasn't really that promiscuous , minus some modifications that were made by rich women of the time revealing some sensitive parts , but obviously that wasn't the general trend .
Another interesting note , is that some Muslim women themselves attempted to circumvent Islamic teachings by creating new outfits that were still quite revealing but which abided by the Islamic rulings of the time on the outside only , those are the only women I found reference to , as they often received comments from companions concerning their "trends" , like some companions forbidding women from some of the new outfits , calling them a bidaa , not abiding by the soul of Islam , etc ..
So to answer your question , if the women were Muslims dressed in non-Islamic clothing , they would get revised / commented-on their outfits by Companions trying to set the pace for the Muslim nation at the time , otherwise if they weren't Muslims , they were most probably completely ignored .
A clue to back that up was that prostitutes remained in some areas of Mecca after the Muslim conquest of the city and they weren't harassed in any systematic way .
Also Muslims were required to guard their sight which wouldn't be necessary if everyone dressed modestly and in accordance with Islam , so it seems that non-Muslims continued wearing the pre-Islamic outfits without any particular disruptions well into the early Islamic era .
For the subsequent Caliphates though , their responses to it were pretty diverse and out of scope of this question.
References (Arabic) :
2) Clothes of Ancient Arabs
Are there English translations available to the material in your links?– AhmedOct 24, 2018 at 11:33
It seems that there isn't unfortunately . Surprisingly it was a tough topic to search for in Arabic , which gives me the impression that it is truly under researched , not sure why though . But as I said , all I found was Arabic sources on the transition period between Jahilliyya and Islam , I think the pre-Islamic clothes part has more English coverage like this question , I found another discussion source but it was a feminist anti-Islamic propaganda thingy .– SongBirdOct 25, 2018 at 21:27