Wonderbar is probably the best bet on removing the glued drywall.
Leaving some drywall glued to the concrete would be a recipe for mold. There is no way to determine if there is a water barrier between the existing drywall and the concrete wall, which I would suspect there isn't.
Remove all the drywall, waterproof the concrete and then add framing and insulation. If you're spending the time to do a complete refinish, that's the best way to prevent future issues.
Leaving some drywall glued to the concrete would be a recipe for mold. There is no way to determine if there is a water barrier between the existing drywall and the concrete wall, which I would suspect there isn't.
Remove all the drywall, waterproof the concrete and then add framing and insulation. If you're spending the time to do a complete refinish, that's the best way to prevent future issues.