You can create jobs in Jenkins that call the TextExecute command line and pass parameters directly. No need to call batch scripts.
For instance a Jenkins job to update the test config from SVN, then run database tests:
cmd /K svn update C:\Testing\TestComplete
testexecute C:\Testing\TestComplete\Acme.pjs "%JOB_NAME%" Database %NODE_NAME% /run /project:Acme /unit:Control /routine:RemoteTest /exit /ns /SilentMode
TestExecute will be aware of all the parameters passed in the command line.
Provided you can work out the correct locations, you can build Log event handlers to convert log messages to a Junit/XML format that Jenkins can understand.
You can also address the Jenkins API directly by creating an http client in TestComplete, giving you full access to job results for aggregation and reporting, etc.