Looking for help with cabinet hinges.

Hello! We are working on a small kitchen remodel and part of it is replacing our old hinges with new concealed face frame hinges. The problem we are running into is the inside of our cabinet doors have a small lip that is causing the new hinges to not be aligned. What would you recommend in this situation?

For reference the doors are 1/4” overlay and they are face frame cabinets. Thank you for your help!