First of all, whether the mortgage you mentioned takes effect depends on whether Bank B has registered the mortgage. For unregistered real estate mortgage contracts, the effectiveness of their creditor's rights is still recognized. If the mortgagor violates the principle of good faith and refuses to go through the registration formalities after signing the mortgage contract, and the creditor suffers losses, he shall still bear the corresponding civil liability, but the civil liability shall be regarded as the creditor's right liability.