correctable error

[Nevadaref]

Shooting the free throws in the wrong quarter is not a correctable error. The timing of when the free throws are awarded is not important, only that they were awarded. The logic of this is backed by what Tony wrote above about shooting free throws in the wrong order. The FED has decided that free throws given at an incorrect time are not considered unmeritted.

It does make me think about the possession to start the 3rd Quarter, though.
If it had been done correctly, the offended team would receive the ball as part of the penalty on the T. But since the free throws were shot before the halftime intermission, and we know that no part of a penalty can carry over from one quarter to the next, I believe that the AP arrow now has to be used to start the 3rd Q.

The determining factor here is that you shot before the 10 minute intermission. The rules book tells us that this intermission takes place between halves (5-5-1), so because the free throws were shot before this intermission they clearly have to be considered part of the first half.
Hence, you are stuck going to the arrow to start the 2nd half.