The background to all this is that Paul had planned to make two visits to Corinth (1:16). This was a genuine intention. However, because of problems that had arisen within Corinth the first visit had proved very painful for all concerned. Therefore, Paul had decided that it would not be in anyone's interests for him to make the second visit so had changed his plans. Now some were stirring up trouble calling Paul fickle and unreliable. When people are being difficult, even rebellious, they will always find excuses to cause trouble. It does not matter what strategies you adopt, what "problem resolution" method you use, someone will find fault. This is the situation that Paul found himself in and it is worthwhile to see how he dealt with it.
First he refers to his own conscience. Our consciences are not totally reliable, nevertheless it is important not to go against our conscience. Elsewhere (Romans 14, 1 Corinthians 8) Paul tells his readers to have proper regard for other people's consciences. For if we go against our conscience we feel guilty, we find it next to impossible to have peace and to act with confidence. So Paul had acted within integrity and in the best interests of others.
Then he made decisions relying on God's grace. We can make the best decisions we can, this does not guarantee success. Our security should never be in our getting everything right, for that is a useless foundation for we are bound to get something wrong at some point. No, our foundation is the grace of God who keeps us from stumbling.
Paul had spent a significant amount of time with the Corinthians (Acts 18), some eighteen months in all, so they knew who he was and what he was like. They had witnessed his life. Personal contacts are vital for overcoming all sorts of obstacles.