The veil represented Beth's modesty and respect. Its removal symbolized the exclusiveness of the marriage covenant.
The Apostle Paul used the veil to picture for us that only when a person turns to Christ, the veil separating him from God is removed.
For until this day the same veil remains unlifted in the reading of the Old Testament, because the veil is taken away in Christ.
But even to this day, when Moses is read, a veil lies on their heart.
Nevertheless when one turns to the Lord, the veil is taken away. 2 Corinthians 3:14-16