“Now he will.” Yahweh speaks about Himself in third person, “he,” distancing himself from the people.
“remember.” This is the idiomatic sense of “remember” that means “remember and do something about” (see commentary on Luke 23:42). In the phrase, “remember their iniquity and punish their sins,” “remember” and “punish” are synonymous. “Iniquity” and “sins” are mentioned in Jeremiah 14:7.