Huh. The Escape action's kind of awful, isn't it?
You attempt to escape from being grabbed, immobilized, or restrained. Choose one creature, object, spell effect, hazard, or other impediment imposing any of those conditions on you. Attempt a check using your unarmed attack modifier against the DC of the effect. This is typically the Athletics DC of a creature grabbing you, the Thievery DC of a creature who tied you up, the spell DC for a spell effect, or the listed Escape DC of an object, hazard, or other impediment.
It seems to suggest -- but does not explicitly state, for what are probably obvious reasons -- that you're escaping by using an unarmed strike, like by elbowing someone in the side of the head if they've put you in a bear hug.
But what good does an unarmed strike do against being tied up? That sounds like it should be a thievery check to untie the rope.
I think they tried to consolidate too many things into a single action here.
Anyway, given my personal vision of this as trying to beat your way out of being grappled or restrained, I'd say whether it has the Finesse trait or not would depend on what kind of unarmed "attack" you're using.