Legal Question in Real Estate Law in California

I hate questions like this because they always depend on facts that you do not know.

A counteroffer is a rejection of the original offer, and a new offer. If the counter offer states how it is to be accepted, then those terms govern acceptance. I have follow up questions to ask you, but no way of asking you them.

I'm in the same position -- wondering what the other necessary facts are. "Signed off by" doesn't really tell us what happened. Who made the counteroffer--the buyer or the seller? No one is "bound" in the usual sense by a counteroffer unless and until it is accepted by the other party in a means invited by the counteroffer. On the other hand, a party that makes a counteroffer places himself in a position where he may find himself bound, if the other party, the offeree, decides to accept. Finally, a counteroffer becomes a contract when it is accepted by the other party. Acceptance can occur, as said before, in any manner invited by the offer (or, here, counteroffer). This is all basic contract law.