13:9 strange teachings. These doctrines, or teachings, apparently maintained that because the readers were not taking part in the ritual life of the temple (v. 13), including the sacrificial feasts, they had no access to God. The author responds that grace, not ceremonial food, strengthens our hearts, for by grace we participate in the worship at the heavenly altar where Jesus ministers.

which have not benefited. Just as the sin offering could not secure cleansing of the conscience (9:9), so also the peace offering could not guarantee that the worshiper had peace and communion with God (Lev. 7:11–18; 1 Cor. 10:18).