Is there an API that can used used to retrieve message transcripts from Messenger?

I don't believe there's an API from Revinitiv. There's an FTP/SFTP feed, which allows you to download XML transcripts once a day. There may be APIs from 3rd parties that can ingest TRMC XML External Feeds. See the link below for more details.
In any case, if you're looking for a solution, the best way to go about it is to reach out to your Refinitiv account manager.
https://financial.thomsonreuters.com/content/dam/openweb/documents/pdf/financial/eikon-messenger-compliance-external-feed.pdf