The correct answer to this open question is the following.
The way in that Mesopotamian culture influenced the Hebrews, Israelites, and Jews was the following.
Father Abraham, the patriarch of the ancient Hebrew people, was from the city-state of Ur, an ancient Sumerian city-state, that was one of the most important in the Mesopotamian times, as well as the city-states of Uruk, Lagash, Nippur or Eridu. Abraham's family worshiped the Mesopotamian Gods, but Abraham believed in one God. That is why he decided to leave Ur with his wife Sarah. He believed that this one god he believed in, had promised the Hebrews a special land for them, and that is when they settled in Canaan, modern-day Jewish territory, close to Judah. That is why Hebrews are also known as Jewish.