What covenant between God and the Hebrews did the Hebrews believe the Ten Commandments reaffirmed?

Well, the first thing to know about your question, is that the term "Hebrews" is considered a derogatory term. Hebrew is a language. "Ancient Israelites" are the people that we read about in the Hebrew Bible (also known as the Old Testament to Christians). Jews today consider themselves to be the direct descendants of the ancient Israelites.

Ancient Israelites considered the Ten Commandments to be only 10 out of 613 commandments given in the first five books of The Bible, which they called the Torah. Although these were considered the most important commandments, because they were written directly by the hand of God Himself, it was important to obey all of the other 603, as well.

When the ancient Temple in Jerusalem was destroyed in the year 70 CE, it became impossible to carry out many of these commandments--and this was when the religion that is now known as Judaism was developed.