Funny, how most people can't see wood for trees.
The money is for risk reduction. Capita must have been on reasonable ground to make the offer, knowing they would move to termination either way. The leaver has the choice to take money, or reserve the right to go down the legal route (often misguided). The company pays the money to remove the risk of later legal challenge.
The fact the amount was very low (10k is low in these situations) must have meant she was a total PITA and they were pretty confident :)