From the first release, the Mobile_Basic template includes two demo resources, logo.png and favicon.ico, that are used as a kind of stubs until user uploads its own files. The logo.png file (just a "My Joomla Site" text) is used in Show in Header: "Logo" / "Logo with site title" modes. And the favicon.ico file (a small "MJ" logo) is used as for mobile site icon until proper one is not uploaded. And the problem was that those files were not created after installation of the Mobile extension, but after a user opens template's Details page, that is quite unclear and unexpected. Now it's happened after the installation and seems to be more clearly.
The favicon.ico file may be uploaded in the Icons section of Mobile_Basic template settings, or by direct overwriting templates/mobile_basic/favicon.ico file on the server.