How can I export the logs of recent run in .tcLogX format (executed tests over a remote machine)

I don't know how the integration with TFS works necessarily, but if it executes via command line, there's a command line switch called "/ExportLog" in which you specify the file name.  If the filenames is given the tcLogX extension, that is how it stores the log.  Information at https://support.smartbear.com/testcomplete/docs/working-with/automating/command-line-and-exit-codes/command-line.html