Disregard (well, some of my above post).
If you go into License Manager, and click "Upgrade" beside each of the products you are renewing maintenance for, you can enter the license key there.
However, this procedure needs to be documented more clearly. Orion NPM has it's own "License" console in addition to License manager. I am not "upgrading" my product either. I am simply renewing maintenance.
Apologies for the confusion. We definitely realize the process can definitely be streamlined. In the near future, you should not have to apply a new key at all. Once maintenance is renewed, your NPM instance will automagically pull down the new license and remove the banner.