Yes, I've extensively studied the covenanting ceremony of that time and how it impacted the 1st century culture. When you read passages about sharing wine, bread, coats, etc. they almost always refer to covenants (such as when Jonothan gave David his cloak, he was passing David his authority as heir to the throne as part of a covenant with David, Elijah giving Elisha his mantle, Joseph's coat are more examples). What Jesus and the people were referring to was the final step in establishing a covenant - "This is my body, eat of it and live." The people of that time would have understood VERY clearly that what Jesus was saying was that unless you entered into a covenant relationship with Him, you had no place in Heaven. So when they asked that question, what they were asking was "By what authority does He offer this covenant?" Jesus is stating EXACTLY what was prophesied in Isaiah, that He would bring a New Covenant. Everything He did was done to establish this Covenant, the Cross, the Empty Tomb, His ascension, His teachings, the miracles, all were pointing to this New Covenant written in our hearts. The people of that time were very aware of this and of what Jesus was saying. It's why the Pharisees hated Him - He claimed the authority to do that which only God could do. Even the forgiveness of sin was part of the Covenant.
You can't study 1st century cultural references from a 21st or even 5th century perspective, you have to study them in light of their culture, not ours.