John Gill Commentary Ezra 4:12

"Be it known unto the king, that the Jews that came up from thee are come to us unto Jerusalem; they are building the rebellious and the bad city, and have finished the walls, and repaired the foundations." — Ezra 4:12 (ASV)

Be it known unto the king
The intent of this letter was, that it might be known to the king what follows:

that the Jews which came up from thee to us are come unto Jerusalem ;
this they observe partly out of contempt of the Jews, having been lately captive in Babylon, and partly to insinuate what ingratitude they were guilty of; that having got their liberty, and come to Jerusalem, they made use of it to the king's detriment:

building the rebellious and the bad city ;
as they suggest it had been to kings, even his predecessors, in former times, (Ezra 4:15)

and have set up the walls thereof, and joined the foundations ;
which was a falsehood; for the most they had done was setting up the walls of their houses in Jerusalem, and laying the foundation of the temple; as for the walls of the city, they had not as yet done anything unto them.