Is it permissible to supplicate for the removal of a friend who causes extreme distress to the one supplicating, knowing that this friend is unaware of this distress?

If the friend is bad, then part ways with him. If he is good, you may leave his company or reduce interaction with him, apologizing gently while giving him his rights and not abandoning him. The aforementioned supplication is permissible if he is harming you or if you are being harmed by his company.