I pulled out my old receipts because I had a lot of accounts with Pinion Management (and I'm a packrat and I save everything). I sent them all my payments via Western Union.
If I were you, I would simply tell them that if they would like to get paid, they will need to either accept payment via Western Union, Money Gram or money order. Tell them you do not have a checking account (even if you do) because they will want to get your new number and start debiting directly from your new account.
If they still refuse all of those payment options, I would tell them that it's their problem. Document the call and the payment refusal. If they want they're money bad enough, they'll accept. If not, don't pay and let it take its course because at that point there is nothing more than you can do.
I had places try to pressure me into giving me a new bank account number even though I lied and said I didn't have one. They kept telling me that I had to have a new account and I told them I did not. I finally told them that they needed to come up with another method of payment if they wanted any of their money back. It took some negotiating but finally they agreed. They will pressure you to no end to get you to give them a new account number but UNDER NO CIRCUMSTANCES SHOULD YOU GIVE IT TO THEM. You will be back in the same situation as you were before.
Hope that helps.