I know this is an old post but I thought I'd respond.

You can integrate to (inbound) TWS using REST API's, the MDM has a built in REST Server which you can test using it's swagger UI on hostname:port/twsd (default port is 31116) to kick off job/jobstreams or just query information.

Integration from (outbound) TWS is done using the REST API job type. I assume Jemtkins has it's own RESTful service.

I'm sure you've sorted this already but wanted to answer anyway.