Just refuse the amendment. You are right. I expect that is exactly what they are trying to do.
I would send a note back saying further to their earlier requedst to cancel the booking 3 days before arrival, you will not be able to accept a last minute amendment either for the same reasons.
Tell them that if they need to change their arrangements you would be happy to consider a new booking for the new dates (if they are available), but they would need to cancel the original booking. Say to be fair to both parties, if you get any of the original dates rebooked you are happy to consider a partial refund for the original dates.