The divorced wife “Then shall she say, I will go and return to my first husband” (v7). But a divorced woman may not remarry the husband who has put her away. He has written her a bill of divorcement, given it in her hand and sent her out of his house. She may go and be another man’s wife [but] her former husband, which sent her away, may not take her again to be his wife (Deuteronomy 24:1–4, Matthew 5:32). But her Husband still loves her: how can He get her back? He must die to redeem her and forgive her (Romans 7:2).
“Thus saith the LORD, Where is the bill of your mother’s divorcement, whom I have put away? ... For your iniquities have ye sold yourselves, and for your transgressions is your mother put away. ... Isaiah My hand shortened at all that it cannot redeem? or have I no power to deliver?” (Isaiah 50:1–2; note the Crucifixion in verses 3 and 6, and Israel’s response, v7–9, cf Romans 8:1, 33–34).
“I will betroth thee unto Me for ever; yea, I will betroth thee unto Me in righteousness, and in judgment, and in lovingkindness, and in mercies. I will even betroth thee unto Me in faithfulness: and thou shalt know the LORD” (v19–20). He will make a new agreement. How? By dying for her, forgiving her, cleansing her by His precious blood, by rising from the dead, and putting His Spirit within her, so that she will never go astray again.
The new covenant “Behold, the days come, saith the LORD, that I will make a new covenant with the House of Israel, and with the House of Judah: not according to the [old] covenant ... which they brake, although I was an husband unto them: but this shall be the covenant that I will make with the House of Israel; ... I will put My law in their inward parts, and write it in their hearts; and will be their God, and they shall be My people: ... for I will forgive their iniquity, and I will remember their sin no more” (Jeremiah 31:31–34). “This is My blood of the new covenant” (Matthew 26:28).
“I will have mercy upon her that had not obtained mercy; and I will say to them which were not My people, Thou art My people; and they shall say, Thou art my God” (v23). So “the strangers scattered throughout Pontus, Galatia, Cappadocia, Asia, and Bithynia, elect according to the foreknowledge of God the Father ... begotten again ... redeemed by the precious blood of Christ ... an holy nation ... in time past were not a people, but are now the people of God: which had not obtained mercy, but now have obtained mercy (1 Peter 1–2). Thus the divorced, exiled, gentilized House of ISRAEL (not Judah), having lost all knowledge of their true identity, are brought into the wilderness (v14), there to find grace (Jeremiah 31:2) and become Christians!