"Ex gratia" is a Latin term meaning something like "as a favor" or "out of goodwill." In general, it refers to something you do that you don't have to do. You do it not out of obligation, but because you want to.
In finance terms, there are a few applications.
In one context, it can mean an additional payment beyond what is contractually necessary. Giving an employee a bonus could be considered an ex gratia payment.
Another context applies to the legal sphere.
Your teddy bear manufacturing company gets sued because you've been stuffing the toys with repurposed asbestos. Eventually, you reach a settlement, but one of the stipulations of the deal states that you don't have to admit any wrongdoing.
You pay $5 million to the plaintiffs, but under terms of the settlement, you weren't actually liable. The payment then becomes ex gratia. At least officially, you paid the money out of the goodness of your heart, not because you had to.
Karma, baby.