Yes they are right, only they can invoke settlement.
1. Until the matter is settled, continue to make Minimum Payments so that your credit history will not be affected.
2. Try availing Loan from your Friends, Family, etc [split the amount] and pay off the Credit Card.
3. Also you can avail Personal Loan for 24+ months tenure at 12% Interest and Pay off the credit card. So when you apply for this, they'll see you are making regular payments on your credit card and it is a very good indicator.
If I were you, I'd borrow some from Family, Friends Personal Loan and first pay off the higher interest credit card.
Best,
Cardbhai