Below is an example of a beauty mark.
(Supermodel Cindy Crawford is known for her signature beauty mark).
If this is not a Colombia's festival, I would interpret "permitting a beauty mark to be dabbed on their faces" as they (the beautiful young women) make themselves look as beautiful as possible. They don't have to literally dab a beauty mark on their faces, though it is quite likely, considering that it was fashionable back then. And if they (these beautiful young women) do, it would be a beautiful mark on their faces.
However, according to the OP's source, January 5 is the Día de Negritos (Day of the Black Ones), and January 6, is the Fiesta de los Blanquitos (Festival of the White Ones). On January 5, boys equipped with black shoe polish chase the girls and try to smear them with their blackened hands. On January 6, instead of chasing the girls with shoe polish, the boys use talcum powder and wheat flour, which turns into a gluey substance when people dump water from their balconies on the victims. So this use of "beautiful mark" is specific to Colombia's festival. And according to what I've seen on the web, it must be the boys who dab those white gluey substance on the faces of the girls.
I can't find a good picture for the Fiesta de los Blanquitos festival (which is supposed to be white), but I can find one from the Día de Negritos festival from this blog post.