Revoke MWS Rights in Seller Central & Reintegrate in Sellics Shortly After
In order to redo the integration with Amazon's MWS API, you'll first need to make sure the MWS Developer Rights in your Seller Central's User Management have been revoked.
After a few minutes, Sellics should then ask you to reintegrate:
Make sure you are in the specific marketplace that you would like to integrate (flag option at the top right), click on "Connect Seller Central Now" and follow the instructions.
Also, to be on the safe side, wait around half an hour after the revoking the rights before attempting to reintegrate. This way the API is sure to be "ready" for a new integration.