Hello Kenta,
the API has a built-in correction mechanism: use the AddTranslation() method to add a sentence pair. Some of the commercial TM tools like MemSource allow the edit using the tool's UI.
You will immediately get the benefit of teh correction in subsequent translations of the same sentence, and you can easily use the correction with the Translator Hub, building a custom translation system that knows your terminology and style for future translations:
https://hub.microsofttranslator.com.
Chris Wendt
Microsoft Translator