They have already filed an arbitration claim against me, why are they still trying to settle outside of court?

Because they would prefer to settle without a hearing. If you owe it, it'll look better if it doesn't end up as a judgement, lien or garnishment against your credit.

Arbitration is something you agree to so they didn't file a claim against you, you agreed to arbitration. This was done because there was no settlement.

They are trying to show that they have done everything they could to settle so that when they go to arbitration they will be seen a reasonable. You need to show that their effort were not moving to try to setlle (but were intended to seem like there settling). Either reject there offer stating why you feel it is not reasonable or make a counter offer. Everything doesn't have to be about money, you can ask for non monetary thing that will make you whole.

If you don't respond they can say look we did everything we could and she ignored our offer.

Because they believe they will come out with more $$$ if they can get you to settle. In the hearing they may lose, and even if they win they have to pay the lawyers. So they think the way to get the most $ is to just settle out of court.