Recovering files from Time Machine backup disk after wrong dd
Sounds like you started to overwrite the drive. The data is probably still recoverable, but, as Graham said, you don't want to do anything to the drive until you attempt to recover the files.

A few options:


While I haven't used it, PhotoRec looks like a good option, if you are comfortable with the command line. Despite the name, it can recover all sorts of file types. It only reads the disk, so your data should be safe even if it is unable to recover it.
For a graphical (and more expensive option), Disk Drill has gotten good reviews. It's pricey at $89, but you can use a free version to preview what it would be able to recover.
If you're in the market for a general disk protection utility, Tech Tool Pro 7 has a data recovery mode. Also, you can set it up to monitor your drives going forward, which would protect against future errors.
DrDD won't completely solve your problem, but it is a graphical way of copying the raw data off your Time Machine drive. I'm not 100% sure that the above programs will be able to read from the copy, but if they can, it would give you another margin of safety. It's also designed to protect your data on failing hard drives, so it should be safe to use in your case.


Hope this helps.