How valid are my prayers after wiping over a transparent and torn sock, assuming it was permissible to do so?

The majority of scholars are of the opinion that wiping over socks is not permissible unless they are thick and opaque. However, others have permitted wiping over them even if they are thin, and this view was favored by Al-Albani and Ibn 'Uthaymeen. For these matters of ijtihad (independent reasoning), one who has acted upon a certain opinion is not required to repeat what he has done based on it if another opinion later appears to him to be more correct, because what was performed was based on a valid ijtihad at the time.