"Registration" implies some governmental entity. If your bank has given you a construction loan, and the loan is secured by the property, they would want a copy of your construction agreement, but that's not "registration."
Your use of the terms "reimbursing" and "investment incurred" is incorrect. Your bank's making a loan, not reimbursing or investing anything, and on one incurs an investment.
What do your construction loan documents say? Have you got a loan broker you can ask about this? If not, and you haven't hired a lawyer to go over your construction loan and contrauction agreement documents, hire one now.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.