Is it permissible to ask a client to try another service without disparaging the competing company's service?

There is no harm in offering your service to someone who has rented a similar service from another party, because the prohibition was reported concerning a Muslim selling over the sale of his brother during the option period. As for renting over the rental, there is a difference of opinion on it, and the Hanbalis have forbidden it, and it is a possibility for the Shafi'is. This is if the rental agreement has not been concluded and has not entered the option phase. Al-Bahuti stated in Kashshaf al-Qina' the prohibition of negotiating a rental after one's brother has negotiated and been accepted, and similarly, renting over his brother's rental during the option of the session or condition. Al-Iraqi said in Tarh al-Tathrib: "The rental may fall under negotiating over his brother's negotiation and selling over selling, as a sub-issue based on the establishment of the option in it."