To reproduce:

1. Spawn a dolphin
2. Give yourself some armor
3. Throw them at the dolphin
   → See the dolphin pick up the armor, but not drop it again like any other item.

Notes:

This applies to other armor too.
The bug is also shown in the nbt of the dolphin in ArmorItems, when you run the command /data get entity @eArmor[limit=1,type=dolphin] ArmorItems