Well, your seals are not any different, they are just missing the felt portion. This felt material degrades after about 3 to 5 years and the surgical tube inside starts dangling around. At that point the whole thing really looks like a mess. I imagine someone along the way just ripped out the felt material. The only thing left in there is the aluminum tape which was the backing for the original seal and gave them some rigidity. It is just held in place with a contact cement. Be careful when you remove it so you don't bend the trip it is adhered to. The slits you see in the aluminum tape make it easier to 'mount' the seal around the curved portions of the roof.
These seals consist of aluminum tape, a black felt type material, and a surgical type tubing inside a fold of the felt type material. This seal does not prevent water from coming through and there is a channel underneath to route the water back to the outside of the roof. I believe these seals mainly close up the gap between the t-top panel and the trim. They also keep dirt and debris out of the water channel and probably cuts down on the wind noise. This seal is fairly easy to replace, allow 3 to 4 hours to do the job if you take your time.
Read this article for the detailed instructions and where to buy the replacement seals.
http://www.magnumgt.com/t-top-seal-replacement/
Good luck and let us know how it goes.
Dave
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Original owner --- 1978 Dodge Magnum XE