Pending means something will happen soon. Maybe there needs to be some action taken first. If a company owes me money and I have asked where my money is I would expect them to say "your payment is pending" meaning they will pay me shortly. We use "under" when action has to be taken "your application is under consideration".

I think you probably have to provide the full context for us to be sure why "under" is used. "Under payment pending" by itself isn't clear.