How does god respond to the israelites encounter with the amalekites at rephidum?

appreciated : )

During the Exodus, when Moses and the Israelites crossed the Gulf of Aqaba and entered the land of Midian, they were met, at a place called Rephidim, by an army of Amalekites. The Bible recounts the events that took place:

Now Amalek came and fought with Israel in Rephidim. And Moses said to Joshua, "Choose us some men and go out, fight with Amalek. Tomorrow I will stand on the top of the hill with the rod of God in my hand." So Joshua did as Moses said to him, and fought with Amalek. And Moses, Aaron, and Hur went up to the top of the hill. And so it was, when Moses held up his hand, that Israel prevailed; and when he let down his hand, Amalek prevailed. But Moses' hands be came heavy; so they took a stone and put it under him, and he sat on it. And Aaron and Hur supported his hands, one on one side, and the other on the other side; and his hands were steady until the going down of the sun. So Joshua defeated Amalek and his people with the edge of the sword. -- Exodus 17:8-13, NKJV.

Just who were these Amalekites, and where did they come from? And what was to be their ultimate place in history?

Origins of Amalek

The Bible dictionary, Insight on the Scriptures, states that Amalek was a "son of Esau's first born Eliphaz, by his concubine Timna. (Ge. 36:12, 16) Amalek, a grandson of Esau, was one of the sheiks of Edom. (Ge. 36:15, 16) Amalek's name also designated his tribal descendants. -- De. 25:17; Jg. 7:12; 1 Sa. 15:2" (Watchtower Bible & Tract Society of New York, Inc. 1988. p. 86.)

While it is true Amalek's name designated his tribal descendants, there is a belief that Amalek dates back BEYOND the time of Esau; and this is backed up by the account of Chedorlaomer and the kings in Genesis 14:

In the fourteenth year Chadorlaomer and the kings that were with him came and attacked the Rephaim in Ashteroth Karnaim, the Zuzim in Ham, the Emim in Shaveh Kiriathaim, and the Horites in their mountain of Seir, as far as El Paran, which is by the wilderness.

Then they turned back and carne to En Mishpat (that is, Kadesh), and ATTACKED ALL THE COUNTRIES OF THE AMALEKITES, and also the Amorites who dwelt in Hazezon Tamar. -- Verse