Making peace to honor God

Matthew 5:23-24So if you are offering your gift at the altar and there remember that your brother has something against you, leave your gift there before the altar and go. First be reconciled to your brother, and then come and offer your gift.
If we only took the time to make peace with those we have offended the world would be a much better place. How many times have you heard people say; "So and so is supposed to be a Christian and do you know what he (did, said etc.) to (me, my friend, my neighbor)..." It is not a very good testimony to God when we leave things unsaid or undone regarding those who harbor resentment against us.
One of the first things I did when I became a believer at age 29 was to go back and apologize and make peace with as many as I could find that I had wronged in life. You may not always be able to reconcile with people. However, it is important that you try your best to do so. How can we pray to God knowing we have wronged others and never sought their forgiveness?