Unless he's put there as a false hope/red herring, Androl is going to find a way out.

OTOH, I hope the solution will something a bit more imaginative than making a gateway to TAR. It would be sort of lame that this ter'angreal, which is very obviously a defensive device, has such an obvious and major flaw. I wouldn't really see the point of the device preventing someone from 'shifting" in and out of the location in TAR if the solution to circumvent the whole system is to enter TAR right next to the dome with army, walk into it and then open gateways to the real world. If the device has such a major flaw, it's all but useless, at least in the days of the WOS. You could open gateways to TAR, from there into the real location and flood it with an army....

I haven't really tried to puzzle out of it works, though logically it seems to "distort" your perception of the Pattern in TAR. I'M not sure i don't think it alters "the real world", at all. My hunch is that since TAR connects all the worlds/dimensions of the Pattern - and it's the only dimension that does that, I think there's an unknown connection between TAR, the way everyone's subconconscious seems connected to TAR, and the ability to Travel. A channeller may use his subconscious to perceive his location in the Pattern, and his subconcious gets this information from the TAR reflection. This may be why it takes a while before you can "learn" the ground, and why this varies from one person to the next.

This would explain all the phenomena. You cannot shift elsewhere outside the Dome, because what you see in TAR is subtly distorted with a matrix from the real reflection. You cannot make a Gateway work for the same reason, because the way your location is reflected in TAR is presently distorted and you cannot "intuitively" learn your location in the Pattern - your subconcious gets the wrong image from TAR.

This would mean the key is a pattern/matrix weave you have to be taught, and which is unique to each dreamspike. So you alter the weave you'd make to open a gateway in this place by adding the key weave to it. This compensates for the distortion of TAR that fools your subconcious, in effect nullifying it and allowing to make the right weave for your gateway. If you try to travel to the place, your gateway might open, but it would open at completely the wrong location.

Perhaps Androl's exceptional skills with gateways. which suggests a great affinity for perceiving the Pattern, will eventually let him overcome the distortion (ie: intuitively puzzle out the key) on his own. He might simply come to realize the gateways he makes are subtly different from the gateways he used to make, puzzle out his subconcious is fooling him.

Since the device prevents Travelling both in and out of the place, I would assume it blocks Skimming to and from the place as well (and obviously gateways to and from TAR would not work either) though since Skimming relies on perceiving where you want to go, maybe Skimming out of an area protected by a dreamspike is perfectly possible.