Is expiation (kaffarah) or something similar obligatory for someone who ordered the throwing away of the Gospel, believing it to be distorted, and then regretted that action?

It is not permissible to throw the Injeel (Gospel) in the trash, due to its inclusion of the mention of Allah and some of His names and attributes, and the names of the prophets. However, the sister who asked the question did not intend to disrespect what is revered, but rather she intended to disrespect human alterations. There is no blame in this, and her remorse and seeking forgiveness are sufficient, for the Prophet, peace and blessings be upon him, said: "Remorse is repentance."