Is it from the Sunnah or an innovation for a group to visit people in their homes, after seeking permission, to remind them of the religion of Allah, especially with men being present when women are also present?

There is no harm in people visiting others to remind them and invite them to Allah, provided that the শরী'আ's (Islamic law's) guidelines and the etiquette of visiting are observed. In fact, this act is among the best means of drawing near to Allah and indicates the high resolve of the doer and his love for good. The Prophet, peace and blessings be upon him, presented himself to the tribes during the seasons, inviting them to Allah and to Islam.