Complex sentence: Its members wished for more frequent communion, not merely attendance at Mass; it wished to relate the eucharist to the world of ordinary life and through its influence the offertory was restored, though not without protracted controversy.
Split into simpler sentences: Its members wished for more frequent communion, not merely attendance at Mass; they wanted to relate the eucharist to the world of ordinary life. Through its influence, the offertory was restored, though not without protracted controversy.