I just had the inside of the wooden frames around my Velux skylights painted. The painter did a good job, but I think when he was removing the masking tape from the skylight's frame, he pulled off a little weather stripping as well: Looking at the rest of the light, this stripping runs all the way around, but is somewhat loosely coupled with the surrounding wooden frame, which makes me think that its main purpose is something other than waterproofing. Most likely its a draft and heat loss barrier, in which case, it's probably not a big deal if a little of it is damaged. Can anyone tell me what purpose this stripping serves and if I should be concerned by the damage to it?
It’s part of the weather-tight system.
It’s not designed to STOP moisture, but rather CHANNEL moisture that may enter during a sever storm. Rather than have beads of water laying along the edge, the plastic cover will channel the moisture to a drip edge on the skylight.
I agree with @J. Raefield, glue it back in place and make sure the edges are sealed.
Nothing on the inside like that would have any purpose related to water entry; if the water got that far in, there would already be damage. That is, at best, just draft and heat loss, but most likely it's just cosmetic. I would just glue it back in place.