For followers of the discussion started last week by Eddie Arthur, here is a definition of "Integral Mission" from René Padilla, "More than a theology, integral mission is an approach to the Christian mission—a way to practice the mission of God in which local churches are viewed as communities that confess Jesus Christ as the Lord of all creation and of every aspect of life and seek to live on the basis of that confession through the power of the Holy Spirit."
René is founder and president of the Kairos Foundation as organisation which “seeks to help the local churches to share the Gospel of Jesus Christ at a personal, social, and community level, not only by means of preaching, but also through all that the church is and all that it does.”
"This approach is presently fostered through a retreat center in Buenos Aires, the Center for Interdisciplinary Theological Studies (CETI, a theological training program with headquarters in San José, Costa Rica), and literature (which includes publication, in association with Certeza Unida, of a one-volume, exegetical and contextual Bible commentary in 2016)."
Please note in the first two quotes the highlighted words "local churches". Also note that the Kairos Foundation does NOT itself do integral mission but rather fosters integral mission by supporting local churches.
So, if a Christian organisation proclaims that it is doing integral mission and all they do is do social work, challenge them to support local churches in their mission.