What is the ruling of Islamic law on taking a commission in exchange for helping a friend obtain a Bar Association ID card, knowing that the person I helped returned the money to his friend for whom the ID card was issued?

It is permissible for someone whose right has been unjustly withheld to pay money to obtain their document, and this is not considered a forbidden bribe on their part. The sin falls upon the one who unjustly withholds and takes. As for what is given to someone who intercedes with their influence, it is not permissible to exchange influence for compensation. However, the intercessor may take a customary fee for their expenses and efforts. If the extraction of the document and the effort involved are permissible, then it is permissible for the mediator to take a commission for their brokerage.