"'However, in the first year of Cyrus king of Babylon, King Cyrus issued a decree to rebuild this house of God. He even removed from the temple of Babylon the gold and silver articles of the house of God, which Nebuchadnezzar had taken from the temple in Jerusalem and brought to the temple in Babylon. Then King Cyrus gave them to a man named Sheshbazzar, whom he had appointed governor, and he told him, "Take these articles and go and deposit them in the temple in Jerusalem. And rebuild the house of God on its site." So this Sheshbazzar came and laid the foundations of the house of God in Jerusalem. From that day to the present it has been under construction but it is not yet finished.'" NIV translation
The exiles continue to explain that their work has been decreed by the former king of Babylon. They point out the fact that, not only did the king authorize the reconstruction, but he had even sent the holy articles for service back to the temple.
"Now if it please the king, let a search be made in the royal archives of Babylon to see if King Cyrus did in fact issue a decree to rebuild this house of God in Jerusalem. Then let the king send us his decision in this matter." NIV translation
A decree of the king (even a previous king that was dead) could not be changed once it was issued. These politicians knew that and hoped that there was no such law on record. Even while this political stuff was going on, God's people continued in His work of rebuilding the temple.
That is a good lesson for us, today, as well. We often see all kinds of political stuff going on that we can clearly see is against the will of God.
During these times, we can choose to worry about the political stuff or we can focus on the task that God has given us.