They almost definitely have an arbitration clause in the agreement, since companies like Amazon, eBay, Airbnb wish to avoid going to court altogether so as not to establish a precedent. This could be favorable to you because they are more likely to settle without either party incurring a lot in legal expenses, but on the other hand it's likely that the arbitration clause asks that each party split the arbitration cost (typically under $5,000 each) regardless of the outcome.

I'm not an attorney but I've dealt with situations like yours. If I were you, I would pursue the arbitration because they are likely to settle.