Backup Disk 'doesn’t contain an EFI system partition'
Unless I'm missing something here it shouldn't be much more complicated than booting into your recovery partition (assuming it's working correctly), reinstalling OS X and then restoring your data from the TM backup on your WD drive when prompted at the end of the OS X installation process.

If you have issues with the recovery partition go for Internet Recovery instead, using Disk Utility to erase your drive before attempting an OS X installation. This will allow the OS X installer to create a new clean recovery partition that should be accessible from CMD + R.

The WD drive should be usable for recovering your data in its present state as Time Machine will alert you the first time you try to use a drive if it has an incompatible file system. As you've made a TM backup the drive must already be correctly formatted. The EFI issue should only really affect you if you are trying to boot from the external drive, which you're not as it doesn't have OS X installed on it. If you've any doubts about your external WD drive then repartition it once you've restored your old data, this should flush out the Microsoft system partition and create a new EFI partition in the correct location on the disk.