The word "he" refers to God, the word "us" refers to the speaker and the hearers, and the word "them" refers to the Gentiles. (See: [[rc://en/ta/man/translate/figs-exclusive]])
God's forgiving the Gentile believers' sins is spoken of as though he cleaned their hearts. Here "heart" stands for the person's inner being. Alternate translation: "forgiving their sins because they believe in Jesus" (See: [[rc://en/ta/man/translate/figs-metaphor]] and [[rc://en/ta/man/translate/figs-metonymy]])