I would most likely grant them points for the drawback, regardless of whether it something the entire party faces, if you intend to run it as an actual penalty. I'm not familiar with the system in question, but my gut instinct would also be to not apply the drawback to the drawback point limit, so they are not stifled from choosing their own unique ones as well.

If they want to take the full 10 points of drawbacks + Teenager, just make sure they pay the price for it.