When you integrate to another system, a good way to do it is to integrate from the gradebook, and do the integration based on idnumber.
That way, if you get a situation like this, you can make a new quiz for people who have not attempted the old quiz, and make a calculated column in the gradebook to combine the grades form the two quizzes, and then switch the integration to use that calculated column.
However, that is not the situation you are in. It is not supported to change the questions in the quiz after some students have attempted it. What I am about to say is purely theoretical, and completely untested, but it might work. Use at your own risk, and you should really test on another server first, with some made up date.
OK, so the way the data structure works is that you have the quiz_slots table in the database, which links quizid to questionid. If you just change the questionid for some questions in a quiz to point to a different question, then it will probably be safe. Note, it is very important. Do not change any of the other values, or delete or add any rows. Also, this will only have an effect for students who have not started the quiz yet.
If you try this, please report back to tell us if it worked.