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christianity steals all kinds of pagan symbology among many other things to claim it as their own, nothing in christianity truly originated from it, always remember this. It's very likely Griffins originate directly from the Sphinx of ancient Egypt and related symbolical creatures of other ancient pagan civilizations. If you look at artwork of the Griffin and Sphinx animal you can see the similarities.


Griffins are representing of freedom and rising to higher levels (soaring high in the sky, the lion half of their soul in the Leo zodiac sign, the sun, success, strength and power). The fact that this dream showed these griffins in a zoo (contained, caged) shows an astral influence in representation of either your own freedom or the human race as a whole being contained or caged, trapped, in that the enemy corrupted our knowledge over the years dwindling us to how the human race is now in it's sorry state. Not to mention you said the griffins were missing their wings, the wings on our souls represent our freedom, to have them entirely absent in symbology means there is no freedom.
You remembering hearing about griffin's having to do with christianity(which is a lie) was you likely picking up on the possibility that this dream was perhaps enemy influenced (in that they were showing you caged and trapped freedom) and this was how you picked up on it, then turning the dream slowly into a revealing nightmare showing you for what it possibly was as either an enemy attack in taunting you on the astral about lacking freedom or even just picking up on enemy thoughtforms that influenced the dream. You may have also generally just caught a glimpse from the astral simply telling you and showing you the state of humanity as it answers questions and ponderings in unique ways like this. We are not free yet, we are firing towards this.
If this dream was an enemy attack then it seems this dream was just the enemy meagerly taunting about how they've 'taken' our freedom (which we're taking back with the full force of 666 burning Suns via the Rituals, etc). Enemy attack or not, don't fall for their ridiculous attempts, I've had actual attacks on me where they've tried this same schtick with me a few times in my own dreams. They're afraid, so they react to try and gain control by making you afraid instead when the reality is they're the one's who are panicking.
You can build up your protection a bit better before going to bed if you'd like just in case, just spend a few extra minutes on your protective aura and firmly believe with intent that it truly does continuously protect you from everything. You can also try asking your guardian demon or Satan for a little bit of extra protection before bed, but just remember to also try to build up your own as well. Remember though, if you ask me this dream could very well have just been the astral showing you something and not an actual enemy influenced event so just don't think that every negative or odd dream like this comes from the enemy as this is largely not the case the majority of the time. You have protection from the gods.
Griffins are very positive. In the origins of the Sphinx specifically, from what I was able to gather in research, it is in representations of the sun and the higher power and the pharaohs in rising to strength. It is a very powerful and positive animal with very beneficial characteristics, do not fall for any lies that would make you afraid of this beautiful symbolical creature.
I hope this alleviates any concerns.