If chase credit card is buying out my ge money bank bill, do they pay with a check?

No, Chase is buying the entire portfolio of cards, so they most likely do not pay with a check, they have negotiated some total amount to pay GE based on some valuation of the receivables. Most likely, the mechanics will be a wire.

To you, nothing will change except the logo on the statements. You still owe the balance on your credit card.