Does the impermissibility of taking commission cease after the company refused to pay for the hours I worked before transferring to permanent employment with them, considering that I was not actually working for them at the time of the agreement with the contracting company?

You are not permitted to take a commission for the aforementioned mediation because it is part of your obligatory work. You must return the amount to the one who paid it to you. Any right you have against the company, you should demand it from them, and this has no relation to the commission.