In the Catholic Church, women wearing veils is a venerable tradition that dates back to the early Jewish-Christian Church. The veil, also known as a head covering (mantilla in Spain and Latin American countries), is a sign of respect and reverence for the presence of God in the church. In addition, it symbolizes a woman’s role as a handmaid of the Lord and her willingness to submit to the authority of the Church.
In the context of the Mass, wearing a veil is a sign of humility and an acknowledgement of the presence of angels and all that is taking place in the liturgy.
Women who wear a veil demonstrate that they are serious about their faith, devotion, and connection to the traditions of the Church. So, yes, women should wear a veil at Mass.