Jamieson, Fausset and Brown on Jeremiah 41:5

5. beards shaven, &c.--indicating their deep sorrow at the destruction of the temple and city.

cut themselves--a heathen custom, forbidden (Le 19:27, 28; De 14:1). These men were mostly from Samaria, where the ten tribes, previous to their deportation, had fallen into heathen practices.

offerings--unbloody. They do not bring sacrificial victims, but "incense," &c., to testify their piety.

house of ... Lord--that is, the place where the house of the Lord had stood (2Ki 25:9). The place in which a temple had stood, even when it had been destroyed, was held sacred [Papinian]. Those "from Shiloh" would naturally seek the house of the Lord, since it was at Shiloh it originally was set up (Jos 18:1).