The connection between Mews (as a PMS) and a channel manager is a 2-way connection. The following document defines both the Mews (as PMS) side, and also defines the API on the channel manager side. The Mews side mainly accepts bookings from the channel manager, while the channel manager side accepts inventory updates from the PMS and then distributes them to connected OTAs.
2-way connection means that both sides of the connection - channel manager and PMS - are required to accept data from the other side in order to correctly connect a PMS through channel manager to all the OTAs. So both sides need to have an open API which the other side has to connect to. Channel manager side accepts Inventory updates (prices, availability, restrictions) and booking confirmations. PMS side accepts bookings.