As a Warlock with the Thirsting Blade Invocation, can I replace one of the Attacks with my pact weapon with a Grapple/Shove?
The only wording difference between Thirsting Blade and Extra attack is: "with your pact weapon"
Thirsting Blade states:
Thirsting Blade, PHB 111
You can attack with your pact weapon twice, instead of once, whenever you take the Attack action on your turn.
If you are using any other weapon other than your pact weapon, you may not attack twice. A grapple is a special melee attack which does not use a weapon, making it mutually exclusive with Thirsting Blade.
The power clearly states that you can make another attack with your boon weapon. It does not say you can grapple. Also it is not am extra attack. So the Invocation is not equal to the fighters extra attack ability.
How ever if you were a 5th level Warlock and a 5th level fighter, you could attack 6 times in one turn.
you can technically use a weapon to grapple and shove people in real life, swords and quarter staffs can be used as grappling bars for hooking, leverage and joint breaking.
So I don't see any problem with grappling or shoving, in replace of an attack as long as you shove/grapple with your pact weapon.