Criminal contempt can be pardoned and Trump has done it before. Police sheriff Joe Arpaio was ordered by a court to end a stop and frisk policy of Hispanic people he put into place because it was racial discrimination. He ignored the order and was charged and found guilty of criminal contempt. Trump pardoned him and offered him a job with the administration.

Civil contempt cannot be pardoned but it only lasts until an order is followed. It's something along the lines of "you will be fined/jailed everyday until you do X".