Jeremiah 41:5 - Joseph Benson’s Commentary on the Old and New Testaments

There came fourscore men, having their beards shaven, &c. “These were tokens of great mourning, by which these persons expressed their grief for the destruction of Jerusalem and the temple. Such expressions of sorrow were forbidden to be used at funeral obsequies, Leviticus 19:27-28; but might be lawfully used upon other mournful occasions. With offerings and incense to bring them to the house of the Lord Some understand this as if devout persons brought their oblations to the place where the altar formerly stood, which they looked upon as consecrated ground; a custom, they think, countenanced by the words of Baruch, chap. Jeremiah 1:10, where the exiles at Babylon are supposed to send money to buy offerings for the altar of the Lord, after that Jerusalem was taken and burned. Others by the house of the Lord understand an altar or place of worship erected by Gedaliah at Mizpah; in imitation of that which was formerly set up there by Samuel, which place continued to be a proseucha, or place of worship, in after times, as appears from 1Ma 3:46. There were many such sanctuaries or places of worship, both in Judea and elsewhere, among the Jewish dispersions.” Lowth.