Is the deferred dower given to the wife based on the intention at the time of the marriage contract that it would only be given upon divorce, or is it a debt that must be paid even if the intention was different at the time of the contract?

If the custom in your country is that the deferred dowry (mu'akhkhar sadaq) is only due to the woman upon divorce, then it is not obligatory to pay it except when she is divorced, and she does not have the right to claim it now. If the custom does not specify the time of its entitlement and no term is set for it, then the marriage is invalid according to the Malikis. It is annulled before consummation and becomes valid after consummation with a dowry of similar value (mahr al-mithl). As for Al-Shafi'i, he considers the dowry invalid and she is entitled to a dowry of similar value, while Abu Hanifa holds that the entire dowry is immediately due. According to the Hanbalis, the marriage is valid and she is entitled to the'mu'akhkhar' upon divorce or death. Given the disagreement among scholars on this issue, the matter should be referred to a Sharia court to examine its details.