Seizure have a fairly wide base of drivers that can cause them. Underlining illness being one of the largest groups!
That being true, being toweled /wrapped / restrained is another as it commonly drives-up core body temperature and heart rate. It is one of the reasons that it is always better to have a trained Avian Professional handle even something as simple as Nail trimming as they have the equipment to support your Parrot when a seizure occurs. Had this happened at a Pet Store this could have been a very different Thread.
It is important to know that our emotions are commonly locked into by our Parrots and as a result it is very important to relax ourselves when we are with them at a Vets clinic.
What to do next time. For you, Relax for the sake of your Parrot. Speak with your Vet regarding what happened last time and watch for a signs of your Grey breathing with greater difficulty, the towel not covering to large an area and generally speaking in softer tones to help comfort your Grey.
Knowing that your Grey is possibly prone to seizure, you should have a discussion regarding likely methods of relaxing your part as there is a high-likelihood that this will occur during other medical activities.
Remember that you are the biggest influencer regarding the emotional state of your Grey!
