I have seen companies outsourcing each phase of SDLC to different vendors. It asks for more collaboration plus strenuous and strict processes to avoid conflicts and ensure smooth running of the project.
- Now an important question to ask:
Are the two activities, design and development happening in parallel with design a little ahead or so?
Or is it that you/development team wait for the requirement analysis and design to finish to embark on development journey?
If both teams are working simultaneously, the best way to resolve conflict is to encourage constant collaboration between the two teams.
You could do agile incremental delivery of your deliverables and involve the designers in planning to understand you interpret the requirements correctly from the design. Also it is equally important to invite design team to the demo/showcase of the completed stories.
If on the other-hand if you are yet to start the development, make sure your team spend some upfront thoughts into the designs handed over to you before starting the development work. It will help the team to figure out if the designs are the best possible and feasible solution for the problem you have. Do a sprint zero kind of activity to derive your key deliverables from the design documents.
Ask design team for clarifications and set up reviews if needed. Establish a solid understanding of the system high level before you code it. You will need to make sure the design team agree on this understanding - otherwise it will turn out to be interpretation error!