Is it permissible to accept a client's offer to pay $75 for the second half of a project that was agreed upon for $80, after $40 had already been paid for the first half of the original project, making the total amount $115, given that the website did not accept his bank card and the client wishes to complete the project quickly outside the platform?

There is no harm in accepting the rent if it has been mutually agreed upon by both parties. The rent is like the price in a sale, and as the Messenger of Allah, peace and blessings be upon him, said: "Indeed, a sale is based on mutual consent." If the first contract is terminated, there is no harm in agreeing upon a new contract with different terms, whether concerning the price or the method of delivery.