I wholeheartedly agree that we impact the culture in which we live - by praying for our communities, the people we are involved in, the businesses in which we work, other activities that we know about.
We impact that culture by bringing God into whatever's going on - bringing his blessing into it.
Where I'd disagree is that it is TWI impacting culture. It's not. It's Christianity impacting whatever's going on. That some of us may first have gained some knowledge of God, of Christ, of Christianity, whilst in TWI, is neither here nor there. It is not TWI that is to be given any glory; it's in spite of TWI. All praise to God and the Lord Jesus Christ for what they do, and for allowing us the joy of serving them.