Is money earned from transcribing cooking show episodes that contain background music considered unlawful gain?

Your work related to writing content for cooking episodes is permissible, and your salary is lawful. However, you must avoid listening to the music accompanying these episodes. If you can remove the music, there is no problem. Otherwise, look for another job free from religious prohibitions. If you are compelled to this work and find no other, then strive to distract yourself from the music, and you will be excused, God willing.