en_tn_lite_do_not_use/jdg/09/19.md

If you acted with honesty and integrity with Jerub-Baal and his house

Jotham offered the possibility that what they did was good, but he did not actually believe what they did was good. Alternate translation: "If you treated Jerub-Baal and his family with honesty and sincerity"

Jerub-Baal

This is another name for Gideon. It means "let Baal defend himself." See how you translated this in Judges 6:32.

his house

Here "house" refers to family. Alternate translation: "his family" (See: rc://en/ta/man/jit/figs-metonymy)