Remove the dross from the silver, and a silversmith can produce a vessel; remove wicked officials from the king’s presence, and his throne will be established through righteousness. (Proverbs 25:4-5 NIV)
This is a picture of a leader taking appropriate action so that his officials and he can serve with integrity.
The picture is of a silversmith crafting a valuable serving piece (like a silver wine goblet).
Dross is made up of other minerals and corrosion that pollutes the silver making it look dull and ugly. They pollute the silver making it hard to recognize and unusable as a serving piece.
Dross is removed through fire. The silver is heated to a high temperature, liquifying it. The lighter dross floats to the top and is easily skimmed off (while liquid) or scraped/sanded/polished off (while solid). The result is beautiful, pure silver that is fit for a king. This is silver of integrity because the impurities are removed.
Speaking of kings and rulers, the point of this visual is that Solomon wants to impress on his son that wicked officials in the king's court are like dross on silver. They mar and undermine the integrity of the king and his staff greatly reducing their ability to serve well.
Removing--not rehabilitating or reforming--is the solution. It's the equivalent of purifying silver through fire.
Compassionate hearts want to give people second chances. This is good! However, discipline is the heat that is needed when wickedness is present. The wicked do not respect authority as seen in their lack of fear of the LORD. This can be costly to leadership. Solomon indicates that wisdom requires the removal of the wicked plain and simple. There's no place for compassion towards one who's heart is far from God even when they are in the presence of God's king or leader.
To serve with integrity is to diligently remove the wicked from your presence giving them no influence on your people.
What is God saying to you?
What are you going to do about it?