In fact, there is the way to run TMS WebOSMaps in offline mode.
Of course you need to have your local tile server, but not only.
Developers are decide to stay this kind of strange hardcode inside of component:
remoteCSS := 'http://openlayers.org/api/theme/default/style.css';
remoteJS := 'http://www.tmssoftware.biz/webosmaps/OpenLayers.js';
remoteJS := 'http://openlayers.org/api/OpenLayers.js';
remoteIMG := 'http://dev.openlayers.org/releases/OpenLayers-2.13.1/img/';
It means, you also need to have your local web-server with support code above, and deceive your operating system like that:
I do not understand why the developers did not specify it in the documentation.