What should I do with the blanket I took from Mina after learning that it was impermissible for me to take it, given the difficulty of returning it?

If you were given the blanket on the condition that you return it after Hajj, then it is a loan (ariyah) and must be returned. If it is not possible to return it, then donate it on behalf of its owner, based on the statement of Shaykh al-Islam Ibn Taymiyyah: "If a person possesses usurped items, or loaned items, or deposits, or pledges, and has despaired of knowing their owners, then he should donate them on their behalf, or spend them on the welfare of Muslims."