Actually, I don’t really understand the system used to disregard the OT. And I mean, in all of Christianity. I always found it strange, for instance, that tithing (at lest, for Protestants) was kept, but that most mosaic laws were just dumped.
To go a bit further in depth with your question. The Mosaic Law covered 2 things, Law of Ritual and the Moral Law.
The Law of Ritual is subejctive to time and place, Noah was under no compulsion to avoid shellfish, but Moses was placed under it.
It’s purpose to was help define the culture of the Israelites and to physically denote them as being set apart. This requiredment ended with the command to preach to all nations.
The MORAL Law, the requirement to worship God as God and no other, to not steal, commit adultery etc… Those commands existed before Moses and will exist for all time. The Moral Law does not change.
Relating back to the topic at hand, head covering are a form of modesty, like almost all attire. While modesty itself is a requirement under the moral law, it applicabiltiy is subjective to time and place. Clothes that are appropriate for sub Saharan Africa are not appropriate for Mass in Stockholm, for example.
In the case of the veil, it was meant to reduce instances of pride in women. In more recent times, in American culture, this particular sin has become less of a concern, so there is very little need to regulate it.
I did note, that in Korea when I went to Mass there on business, every single woman was veiled. There were teen age girls in sweats and jeans, but wearing a veil. I never enquired, but it might be paritcular (diocesan) law there.
(side note, in was from the Cathedral gift shop in Korea that I got my wife her first veil, she had expressed interest before, so I brought one home)
But I digress …
It (as has been show from Dr. Peter’s website) a canonical requirement does not exist for the Universal Church, but it still remains a item of modest attire that a woman may freely choose to wear.