The Case: Little Sisters of the Poor v. Pennsylvania
The case concerns regulations under the Affordable Care Act that requires employers to provide women with “preventive care and screenings” without “any cost sharing requirements.”
The Little Sisters of the Poor objected and sued. The Little Sisters are an international congregation of Roman Catholic religious women who have operated homes for the elderly poor in the United States since 1868. The Little Sisters hold the religious conviction that deliberately avoiding reproduction through medical means is immoral.

The nuns were required to offer services that violated their beliefs. For the nuns, it wasn’t a money question, but a moral one. They compared their plight to high schools that remove soda machines because they don’t think soda is good for children:
It doesn’t matter that the soda companies will pay for the machines. And the school’s decision doesn’t prevent children from getting soda elsewhere. The school simply doesn’t want to be responsible for providing something it believes is bad for its students. It is the same with us.
Constance Veit - Little Sisters of the Poor
The Federal Government arrived at a solution that exempted the Little Sisters from the source of their concerns.

The states of Pennsylvania and New Jersey challenged the Trump exemptions, arguing that they were not authorized by the Affordable Care Act and the Religious Freedom Restoration Act. The case went to the Supreme Court of the United States. Here is what was the Court had to say:
No language in the statute itself even hints that Congress intended that contraception should or must be covered.
Thus, it is Congress, not the Departments, that has failed to provide the protection for contraceptive coverage that the dissent seeks. The only question we face today is what the plain language of the statute authorizes. And the plain language of the statute clearly allows the Departments to create the preventive care standards as well as the religious and moral exemptions. We hold today that the Departments had the statutory authority to craft that exemption, as well as the contemporaneously issued moral exemption.
Justice Thomas - Opinion of the Court
In a nutshell: The Trump administration had legal authority to allow private employers with moral or religious objections to opt out of providing birth control health insurance required under the Affordable Care Act.
Here is the Decision: https://www.supremecourt.gov/opinions/19pdf/19-431_5i36.pdf