So first you have Eldritch Scythe:
Then you have the wording on Extra Blast:
Then Thirsting Blade:
This isn't nitpicky..this is the last 7 years of 5e, and having to interpret things this close to the wire. So here is the breakdown that I also read into this.
1. You choose on your Action...
In the official errata it was clarified that Invocations are gained at warlock levels only. So it's class levels...not character levels.
(do a google search for "5th Edition Errata" since EnWorld won't let me post the damn link because I haven't earned my big boy pants yet....FFS)
Spellsheet 4.011
I added Warlock level 7 and chose Great Old Ones. It then shows me my list of automatic spells. When it generates the sheet, those spells are not added.
If I tell it to manually let me select my spells, they are not "X" selected there either.