They care because the coins were never issued. They were stolen. Even when a 1933 Double Eagle coin was legally auctioned, an additional $20 was needed to “monetize” the face value of the coin so it would become legal currency.
If you make it to page 5, there's a note that these coins might have been issued by the Mint, officially but not legally. There's a brief window of time after FDR's gold recall order that tellers at the Mint were trading gold coins for the recalled bullion. It is entirely conceivable that some 1933 double eagles might have been issued as change.
If it's true that they were stolen, then we're beyond the statute of limitations for obtaining criminal justice. Now we're back to the feds attempting to recover the property of Uncle Sam and it's a pittance of gold. No longer worth the effort.
Edit: I think I fat fingered the wrong reply link. It's not worth it to move the comment.
IANAL but I would assume the Government's argument would be that the crime is ongoing and that after becoming aware of the coins they made efforts to recover the property.
It is a pittance of gold but thats not the point. The Mint believes these coins were misappropriated and it's their duty to secure the money supply. If I were the Government I would offer $20 per coin, as thats the face value of the coins. Although that might not be possible if that technically monetizes them into legal tender.