Oh. Okay. Then lemme try this way:I just explained the argument for why that wouldn't work. The Invocation specifies both attacks are with the Pact Blade. It's about what effect gains trump through being the more "specific" rule in "specific vs general".
If Thirsting Blade is the more specific, it doesn't work. If Eldritch Scythe is, then it does.
EDIT: At least I think that's the argument, because that's the only thing that could maybe make them not work together.
Thirsting Blade states you get to make 2 attacks with your pact weapon on your turn instead of 1 "When you take the Attack Action."
Eldritch Scythe specifies that you can use it "When you would use a weapon attack as part of the Attack Action or an Opportunity Attack"
Further, Pact of the Blade itself says that if your pact weapon has a bonus you can apply it to your Eldritch Blast or Ray attacks.
Eldritch Scythe is an attack replacer that still uses the base weapon (If it's a pact weapon it also gains bonuses). So you swing your Pact Weapon and the Eldritch Scythe appears around it. Because you're -using- your Pact Weapon to make a Weapon Attack as part of the Attack Action. It's a Weapon Attack, not an Unarmed Attack.
Does that solve it?