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You are in contract negotiations.
While they may have previously made an offer, they can rescind it. While their recission at this point is only oral, it was communicated.
Thus, I think you would have hard time enforcing an offer than you agree was verbally rescinded.
Personally, I would send payment, along with a copy of their prior offer and a statement that payment is sent as your acceptance of their offer.
It would then be up to them to accept by depositing your payment, or reject with a statement that their prior offer is no longer in force.