When you use Wrath of the Storm with Thunderbolt Strike, the creature that attacked you is pushed back immediately. From the section on reactions:
If the reaction interrupts
another creature’s turn, that creature can continue its
turn right after the reaction.
The creature doesn't get to finish its turn, then get hit by your reaction - your reaction happens straight away, interrupting their turn. So if you use Wrath of the Storm + Thunderbolt Strike on the 1st attack of a Multiattack, the creature will be pushed back 10 feet.
Then, if it has movement remaining, it can move up to you and finish its Multiattack sequence. If it does not have enough movement to get back within reach of you, it will have to either end its turn without completing its Multiattack, or take the other attack(s) on a creature that is within its reach.
To start with, your familiar can't use Shocking Grasp. Find Familiar says:
Finally, when you cast a spell with a range of touch,
your familiar can deliver the spell as if it had cast the
spell. Your familiar must be within 100 feet of you, and
it must use its reaction to deliver the spell when you cast
it.
So you use Shocking Grasp, and your familiar merely delivers it. This all happens on your turn, too, not your familiar's turn.
However, this is a good thing for you, because Thunderbolt Strike says that:
At 6th level, when you deal lightning damage to a Large
or smaller creature, you can also push it up to 10 feet
away from you.
So the fact that you cast Shocking Grasp, and you damaged a creature, means that you can indeed use Thunderbolt Strike to push it away from you.
Note that that's away from you, not away from your familiar: Your familiar delivers the spell, but you still cast it, and you dealt the damage. If that wasn't the case, you wouldn't be able to use Thunderbolt Strike at all.
Best Answer
No, you can't push a Lightning-Immune Creature using the Thunderbolt Strike Feature.
As I read the feature and understand the mechanics, an immune creature cannot take damage from whatever it is immune to. Therefore, effects which depend on damage cannot take place against said creatures.
I think this would be a fine interpretation if the description read "when you hit a creature with a spell that deals Lightning Damage", because there's no requirement in that description that actually requires the creature to take damage, but here, I don't think that's the case.
The alternative reading is to infer that Immune Creatures "reduce damage by 100%", implying that the creature takes "0 damage", and thus still qualifies. But I think that's a weird reading, and I think my overall conclusion, that immune creatures do not trigger "when damaged" effects, stands. My interpretation is also supported by Crawford, who asserted that taking 0 damage means taking no damage, and specifically used this feature as an example of an effect that would not trigger on a creature immune to the damage type.