Must the money be returned according to the agreement with the site owner, based on the specified rental value for the months during which the advertisement was benefited from without his knowledge?

If the owner of the site does not forgive you for your transgression against him, then along with repentance, you are obliged to pay the fair rental value for the period during which you rented the site without his knowledge and permission. This is because you are considered in the position of one who usurps property and then rents out the usurped item, and such a rental agreement is void. You are therefore responsible for guaranteeing the fair rental value. As for what you later agreed upon regarding renting the space for a known fee, there is no impediment to that.