It must be borne in mind that the book of Deuteronomy forbids only blood sacrifices outside the central sanctuary: “you must bring everything I command you to the site that the Lord your God will choose to establish his name: your burnt offerings and other slain offerings, your tithes and contributions, and all choice votive offerings that you vow to the Lord” (Deut 12:11; cf. vv. 6, 14, 27). Even H, which prohibits all worship outside the Tabernacle, in effect, also limits itself to blood sacrifices: “If any person of the house of Israel or of the aliens who reside among them sacrifices a burnt offering or another slain offering, and does not bring it to the entrance of the Tent of Meeting to offer it to the Lord that person shall be cut off from his people (17:8-9). Thus, all cultic laws in the Bible that prescribe that legitimate worship is possible only on one authorized altar (cf. Josh 22:23) limit this prescription to blood sacrifices without even mentioning incense.
Positive evidence of an independent incense offering can be derived from the fact that “eighty men came from the Shechem, Shiloh, and Samaria, their bears shaved, their garments torn, and their bodies gashed, carrying cereal offerings and frankincense to present at the House of the Lord” (Jer 41:5)—after the Temple had been destroyed! This event gave rise to the later ruling, “R. Gidel said in the name of Rab: (even) after an altar is destroyed, it is permitted to offer incense at its site” (b. Zebaḥ 59a). T. Levi, composed at the end of the Second Temple period, speaks of “archangels” who serve and offer propitiatory sacrifices to the Lord (in the heavenly sanctuary) on behalf of all the sins of ignorance of the righteous ones. They present to the Lord a pleasing odor, a rational and bloodless oblation (T. Levi 3:5-6). Thus, at all times, regardless of whether the Temple was standing or destroyed, it was not uncommon for the people to worship the Lord at that site or anywhere else by means of incense offerings.
Only against this customary background is it possible to explain the request made by Elephantine Jewry of Bagohi, the governor of Judah, Johanan the high priest, and his colleagues, the priests, to rebuild their temple: “they shall offer the cereal offering, incense and burnt offering on the altar of God” (Cowley 1923:30.25; cf. 30.18-21; 31.21, 25, 27). From Bahohi’s response, it follows that permission was granted except for the burnt offering (Cowley 1923:32.9-10). The Jews of Elephantine accepted his terms: “n[o] sheep, ox, or goat is offered there as a burnt offering, but only incense, cereal offering, and [libations].” (Cowley 1923: 33.10-11; cf. Porten 1968:291-92). Thus both the religious and civil authorities, Jews and non-Jews alike, permitted bloodless sacrifices outside Jerusalem, including incense. (Jacob Milgrom, Leviticus 1-16: A New Translation with Introduction and Commentary [AB 3; N.Y.: Doubleday, 1991], 629-30)