When putting Banette into the Lost Zone with its "Puppet Offering" Ability, do you also put the underlying Shuppet card into the Lost Zone too?
Yes, the underlying card is part of the Pokemon; it is not "attached to" the Pokemon.
Puppet Offering

Other known variants


x2
-30Puppet Offering
Once during your turn, you may put a Supporter card from your discard pile into your hand. If you do, put this Pokémon in the Lost Zone. (Discard all attached cards.)

Spooky ShotResentment at being cast off made it spring into being. Some say that treating it well will satisfy it, and it will once more become a stuffed toy.
When putting Banette into the Lost Zone with its "Puppet Offering" Ability, do you also put the underlying Shuppet card into the Lost Zone too?
Yes, the underlying card is part of the Pokemon; it is not "attached to" the Pokemon.