Was playing a casual game the other day at the LGS, and neither one of us really knew the answer to this question.

I was flying Tel, and they had a Decimator with the Vader crew on board. Now, if the Decimator were to kill off Tel with its regular attack, and Tel's pilot ability activates to keep her alive, can they still use the Vader crew ability on Tel after she has returned to life? We both assumed yes, because Tel isn't actually dying, it's "if it would kill Tel" discard all damage cards, so I assume it all falls under the same phase and they could still Vader for an additional damage.

Even though we both agreed on it, just trying to get some input from an outside source in case there is something we're overlooking.

I would view it that way where he does additional damage, thus countering Tel's ability.

Purely because Vader's card says "after you attack" which indicates the attack is completely over, and Tel's skill says "upon receiving damage" which means the attack isnt over.

Is a destroyed ship technically removed during an attack or after an attack?

After an attack, Tels ability kicks in before she is destroyed.