You would have done well to include the last four verses of the first chapter:
But the one who gives us security with you in Christ and who anointed us is God; he has also put his seal upon us and given the Spirit in our hearts as a first installment.
But I call upon God as witness, on my life, that it is to spare you that I have not yet gone to Corinth. Not that we lord it over your faith; rather, we work together for your joy, for you stand firm in the faith.
2 Corinthians 1:21-24
This introduces a series of references to anointing or the Anointed.
First, he refers to his actions as service, not lordship, and service that is full of pain (suffering of the Cross), but a pain that he shares with the Corinthians.
Then in 2:14 he starts describing the experience of anointing “manifests through us the odor of the knowledge of him.” The aroma is us, we are the sweet smell of the chrism, a smell of death and of glory.
Then comes ch. 3, starting with the comparison of anoitning to the act of smearing ink on he akin of parchment. He has anointed the Corinthians like their skins are the parchment , so they are his letter, and the Holy Spirit is the smell of the oil, the Spirit that gives life.
Then he compares this letter to one engraved on stone, like the words of God entrusted on engraved stones to Moses. Moses became radiant throuh his encounter with God, a radiance visible in the Law, the engraved stones, but veiled.
We with unveiled faces, have encountered God in Christ and received not engraved stones but the Holy Spirit, which is knowledge and beauty and courage etc. We have become radiant, glorious by reflecting the image of the Anointed Jesus.
Chapter 4 continues the theme by talking about possessing this treasure, the anointing, the oil, the writing, in clay vessels that are not up to the great value placed inside them.
This is my mangled version of an interpretation that can be found in several sources. St Paul is talking about how God has “put his seal upon us and given the Spirit in our hearts.” (1:22) It is a minority interpretation, more common in the East than the West.