Of course that was a federal land claim on a confiscation of land taken for military purposes. The confiscation of land over taxes after the war by the Arkansas State Government would not come under that program. I came across an old family trunk many years ago and one of the more unusual things in it was the taxes reciepts that the family had paid for 1861, '62. '63' and '64 to the state of Arkansas Confederate Government and in 1865 the taxes they paid to the Arkansas US Government for back taxes for those same years and 1865. They evidently were some of the few lucky ones to have the ability to pay those taxes.
The Southern peoples paid for that war in many ways and some of them were most dear. That is the reason that the Sharecropper land/farming system came about and just one of the many reasons why the South did not recover from that war until recent times.
Just a political point of view but the south doesn't owe anybody "reparations" for anything. Just like the SCV camp member that made the claim for the destruction of his family property. Reparations have "Historically" already been paid to earlier generation. If anything, as you said, it is the decendents of those southerners who are owed the reparation for having an "Illegal" war thrusted upon them the same as the Native Americans and the taking of their lands.