Brant A. Gardner discusses the use of "church" in the Book of Mormon; argues it is an example of a translator's anachronism.
Brant A. Gardner, Second Witness: Analytical and Contextual Commentary on the Book of Mormon, 6 vols. (Salt Lake City: Greg Kofford Books, 2007), 3:338
“Church” is the English translation for the Greek ekklesia, but of course, Mormon would not have written ekklesia on the plates. How could there be a church in the Book of Mormon before there was a church in the New Testament? The Greek word means a group of citizens called out to assemble for political purposes, outside of the religious use of the term. It is used in the Septuagint interchangeably with “synagogue” to translate the Hebrew word for “assembly.”
Although the Hebrew qahal “assembly,” could be the basis for the translation to the English “church” in the Book of Mormon, any argument based on specific words in the Book of Mormon ignores the problems of translation. We do not know what word Mormon wrote. We know only that Joseph Smith translated it as “church.”