You are correct that the SAP ECC connector is only supported for source capabilities (Copy activity source or Lookup activity).
Writing to a sink not supported by ADF will required additional work outside ADF. You can use ADF to write your API data to an on premise file store or database, but you will need to implement a second step to get the data from the file store/database and into SAP ECC. The second step will need to be implemented in a technology which includes a capability to update SAP ECC directly.
Alternatively, you might choose to link Teamcenter and SAP ECC directly, using some other technology and avoiding ADF completely.
(I don't know much about SAP ECC; I can't comment on what technologies you might use to interact directly with the product).