This would seem to be a question of ani mehapech becharara. A cleaning lady doesn’t have an exclusive contract, but it is understood that if she regularly works for someone, she usually will continue that relationship for the long term therefore, if one grabs her away it may fall under the category of ani mehapech becharara.
There is a relevant disagreement between Rashi and Tosafos about the parameters of ani mehapech becharara:
- Tosafos says that ani mehapech becharara only applies in the case of a purchase. If one person is exerting effort to try to buy an item, a second person is not allowed to interfere and usurp the deal. The reason is that he has the option of purchasing the same product elsewhere, so it is improper to obstruct someone else’s purchase; however, if one person is trying to take control of an ownerless item, Tosafos says that a second person is not prohibited from grabbing the item away before the first one gets it. Since there are no other opportunities to get this item for free, the second person cannot be told to leave this specific item alone and get it from somewhere else.
- Rashi disagrees; he says that ani mehapech becharara applies even for ownerless items and therefore it would be forbidden to grab away such an item from one who has already exerted efforts to get a hold of it. One who does so would be labeled a rasha.
The Shulchan Aruch states that if someone employs a melamed to tutor his son, someone else who wants that teacher to tutor his own son is allowed to offer him higher compensation to solicit his services. The obvious question is, why is this not a transgression of ani mehapech becharara?
The Sm”a explains that a good teacher of Torah is a unique item; not all tutors are equal, and some are more adept at explaining the subject matter than others. Therefore, the melamed can be compared to an ownerless item, of which there are no other opportunities to find, and there is no prohibition to lure him away.
We see that the Sm”a understood the Shulchan Aruch to be ruling like Tosafos, that ani mehapech becharara does not apply to unique opportunities, and explains that the differences between teachers deems them unique entities that cannot be obtained elsewhere. He states that they cannot be compared to houses or vessels which are all relatively similiar. The subtle differences between them are not enough to consider them sufficiently unique to the point that the prohibition would not apply.
This leads us to our case of whether cleaning ladies are considered unique, and are unavailable elsewhere. While it may be easier to lure away your neighbor’s cleaning help, it probably would be possible to find an alternative cleaning lady by exerting a bit of effort to search elsewhere. One may claim that this woman has a particular knack for exemplary cleaning, yet often the difference between her and the next cleaning lady is not really that pronounced, and the one trying to solicit her may be making this claim out of emotion rather than intellect.
It is important to bear in mind that Rav Moshe Feinstein writes that one who fears Heaven should be stringent like the opinion of Rashi and should not interfere when he sees someone else exerting effort to obtain an ownerless item. Presumably, he does not expect one to adhere to this stringency in the case of the melamed because one must always be concerned about his own ruchnius.
Having said this, I would permit one to draw away a Chumash tutor by offering him a higher wage, but I would be very reluctant to permit someone to lure away someone else’s cleaning lady.