The most important rule of training is that parrots do not learn from negative reinforcement. Any unwanted behaviors should be ignored completely and desired behaviors should be rewarded. The best thing to do when she makes the noise is to quietly leave the room. By covering her, she is still getting attention because you have to approach the cage to cover her. In some cases, you can keep the back of the cage covered in a way that you can flip the cover over the rest of the cage without her seeing that you did this. For this to help at all, it must be instant, and she can’t see you. It’s just a way to get her attention and hope she connects the cage cover flipping down when she makes the noise. But again, praise and treats work better. Reward her with treats and attention when she makes sounds or words that are OK with you. But do not try to make her say them instead – meaning if she makes the alarm sound, do not go to her and talk to her or encourage words. Ignore her until she is quiet, and then immediately go to her and reward her for being quiet. Then you can talk to her and encourage talking or a more pleasant imitation. Greys love to mimic sounds, so most do make alarm and related sounds. It’s fun and they hear them a lot! Maybe record a bird singing or other less annoying sound for her to learn instead of the alarm. Training can be slow, especially training out a bad habit. But you must be consistent. Every time you give in, such as telling her to stop, you undo any ground you have made. Be patient and no matter what, give her no reaction to the alarm sound other than quietly leaving the room.
Thank you for asking Lafeber,