The Marketing Cloud API documentation says that the Transactional Messaging API does not support suppression lists or exclusion scripts.
However, the Transactional Messaging API does support auto-suppression lists. If someone is on an auto-suppression list, and the CAN-SPAM Classification Type is set to ‘Transactional’ or ‘Both’, they will not get an email sent via the Transactional Messaging API.
This can be verified if you have the Event Notification Service configured. Check the ‘reason’ why an email was not sent:
reason: ‘The subscriber was excluded by a suppression list’