A babysitter who worked on Shabbos ONLY for a Jew and it is not possible for her to work on weekdays, as well (or to provide some other service) – it is forbidden to pay her.
May the one for whom she babysat take the money that is “owed” and put it on the table and declare it hefker, and then she will pick it up and take it? If yes, may one always do this l’chatchila (she will work for free and then the mother will put the money down and declare it hefker), or only b’dieved if it happened already?
Although it would sound technically alright, this would be similar to giving it as a “present”, which is problematic . if it is being done, when it is blatent, that you really mean to pay the person for thier shabbos work.
See Orchos Shabbos 22 ftnt 151, that it is only permitted to give the sechar shabbos as a present when it is isn’t blatant and clear that it is pay for the work of shabbos. Even if you will want to argue on this, it surely is not l’chatchila to make a harama to be mevatil the takana of chazal. Also see Piskei Teshuvos 306-10.