it seems as if they are winging it. What they are saying is that their own water taxi is on strike, and they will try to find you a ride from another taxi boat company. And then they will say, "all of them went on strike, we couldn't help it."

If in your shoes, I would choose between 2 possibilities. If you are not just staying in Venice for 1-2 days, find a place to eat and do things where no transportation is needed. That would include everywhere in Venice, because anywhere you walk around will be magical. You don't have to go to Giudecca.

Or, if you have to go to Giudecca for that particular restaurant that may have some sentimental value that I won't question, I am 95% sure that during the strike there will still be boats back and forth between Venice and Giudecca. Giudeccani children have to go to and from school, and so the vaporetti will run during the most important periods, despite the strike.

The strickers are trying to get the federal government to give them more money for job creation. They do not want to push the average citizen to be against them, so every strike has some exceptions to not affect the locals too much.

There will be some boat service between The Giudecca and Venice. Strikes do not leave people having to sleep under a bridge. So, despite the strike, I am sure you can still go back and forth to the Giuedecca a few times a day.

However, if I were you I'd just stay in Venice that day. That is because although there must be service to Giudecca, it might only be to accomododate workers hours, and you will have long waits.

The response Gritti gave you, if your post is accurate, is that their private boat won't operate, and they will try to find somebody else. Then, they will say that nobody else was available due to the strike. They didn't want to say no, and make you cancel.