This memorial in most all the links I could find do not refer it as the Reconciliation Memorial. It is almost always referred to as the Confederate Memorial.
This history of it tells maybe why that is:
https://www.arlingtoncemetery.mil/Explore/Monuments-and-Memorials/Confederate-Memorial
I think it is stupid to tear it down, teaches nothing but hate, and I think all soldiers killed in wars deserve a place for visitors to mourn them. They die for the causes their political leaders devise, and it is mostly from loyalty to those whom they belong, more than political causes, that they fight.
In 1898, when the Spanish American War erupted, former Confederate states supplied important U.S. forces, “burying the hatchet,” to fight along-side former Union foes. Reconciliation and teamwork between the Northern and Southern soldiers facilitated a swift victory in that war—lasting only four-months.
President McKinley, a Union army veteran, recognized this healing that made the military exemplary. He told the nation, “Sectional feeling no longer holds back the love we bear each other… The Union is once more the common altar of our love and loyalty, our devotion and sacrifice.”
In June 1900, McKinley supported a bill to establish a Confederate section in Arlington Cemetery. That resulted in the reintering of some 260 Confederate bodies from various burial places to a designated section of Arlington Cemetery. A few years later, Secretary of War William Taft received a request for erecting a monument in that Confederate burial area—Section 16. In 1906 it was granted.
Moses Ezekiel, a world-renowned American sculptor, the first Jewish cadet at Virginia Military Institute who served in Confederate army in the Civil War, was chosen to create the monument that would capture the fullness of the spirit of reconciliation, serve as memorial to the hundreds of dead Confederates buried in Section 16, and be recognized as a prominent “Peace Monument,” commemorating the reunification of the North and South.
https://www.discovery.org/a/why-preserve-the-reconciliation-monument-in-arlington-cemetery/