en_tn_condensed/1sa/06/03.md

the God of Israel

Possible meanings are 1) they were speaking the proper name of the God of Israel or 2) they believed that Israel worshiped one of many gods, "the god of Israel." See how you translated this in 1 Samuel 5:7.

by all means send him a guilt offering

The words "by all means" are a forceful way of saying something. Alternate translation: "you must send a guilt offering" (See: rc://en/ta/man/jit/figs-idiom)

you will be healed

"you will no longer be ill"

you

The pronoun "you" is plural, referring to all of the Philistines. (See: rc://en/ta/man/jit/figs-you)

why his hand has not been lifted off of you

Here "hand" is a metonym used to represent God's power to afflict or discipline. Alternate translation: "why he has not relieved your suffering" (See: rc://en/ta/man/jit/figs-metonymy)