The Talmud in Sanhedrin (99b) states:
בעיא לאיגיורי באתה אצל אברהם יצחק ויעקב ולא קבלוה הלכה והיתה פילגש לאליפז בן עשו אמרה מוטב תהא שפחה לאומה זו ולא תהא גבירה לאומה אחרת נפק מינה עמלק דצערינהו לישראל מאי טעמא דלא איבעי להו לרחקה
Timna sought to convert. She came before Abraham, Isaac, and Jacob, and they did not accept her. She went and became a concubine of Eliphaz, son of Esau, and said, referring to herself: It is preferable that she will be a maidservant for this nation, and she will not be a noblewoman for another nation. Ultimately, Amalek, son of Eliphaz, emerged from her, and that tribe afflicted the Jewish people. What is the reason that the Jewish people were punished by suffering at the hand of Amalek? It is due to the fact that they should not have rejected her when she sought to convert.
Per this Talmudic piece, since Yisrael "struck the first blow," Amalek is/was 'justified' in causing Jewish suffering.
And yet we have a mitzva to destroy Amalek. Is this because of the suffering they cause? If so, what gives?
