To me, this verse describes what happens to us when we place ourselves on God's altar. On His altar there is a two-fold action that takes place.
 
First, God has to remove some stuff out of us. We all have things in us that God needs to extract. In the verse above, falsehood and unfaithfulness are the two things that the Psalmist is requesting that God take out of him. But, there are many more things that we want God, as the Master Surgeon, to remove from us. I bet you can think of a few things you'd like God to take out of you.
 
Secondly, there are many new and beautiful things that God needs to impart into us. One such thing that comes to mind is when David said, "Renew a right spirit within me."  Psalm 51.  So, on one hand, God is taking stuff out of us, and on the other hand He is putting good things into us.
 
This is what happens to each of us throughout our life as we continually walk with God. He is always working deep on the inside of us. God works from the inside out, not the outside in.
 
You need not fear God's altar. It is the place where the best work is done within us. When we've been on His altar, we are better people.
 
Put yourself on His altar today and pray, "Lord remove bad things out of me and impart great things into me, for your glory!"