Am I obligated to pay the visa fee for Umrah for someone who did not clarify the visa's validity period, which led to my parents not traveling, especially since he is supplicating against me?

If the agreed-upon visa duration is a full month, or if custom dictates it, then you are not obliged to pay the fees unless the visa is issued for that duration. However, if the duration was not agreed upon and custom does not dictate it, then the contract is not valid unless the type or duration of the visa is specified; due to the uncertainty of the benefit. "Leasing is a sale, and a sale is not valid unless the quantity is known." If the lease is فسدت (invalidated) and the lessee has not received the benefit, then no rent is due from him.