Is it permissible to participate in an examination for female Qur'an memorizers that entails a reward, even though one of the new conditions for the examination is not met by the examinee, and is it permissible in this case to take the examination but refuse to accept the reward?

Firstly: The association is permitted to change the terms of the competition or cancel it, because a competition contract is among the permissible (جائزة) contracts, not binding (غير لازمة). Either party may revoke it as long as the work has not commenced. Similarly, the one who sets the prize may increase or decrease it before the work begins.

Secondly: It is obligatory to inform the association that the condition does not apply to you. If they permit you to take the test, then that is fine; otherwise, you are not allowed to enter. Your joining the study circle based on the conditions being met for you does not obligate the association to maintain the initial conditions, as the competition is a separate contract from the matter of joining the study circle.