Any such policy would need to be specified within the lease to be enforceable. If there is nothing in your lease that mandates a bespoke payment method, call their bluff and just pay by check.

There are real issues with incomprehensible leases and terms of adhesion sprung late in the process, but it behooves us to keep focus on the specific contours of the problem so the people who are able to push back on such nonsense can better do so.