Etherwave repair question

Hi everyone, I have made a terrible mistake. 

While trying to tune my Moog Etherwave Standard (had a reverse-pitch problem), I have damaged one of the ferrite coils. I was using a metal Allen key, I didn't know I had to use a plastic one. 

I am planning to buy a new Allen key from https://www.coilcraft.com/en-us/tuningtools/ as you have recommended. 

Could you point out where I can buy a new ferrite coil? 

Plus: what do you think is the best way to extract the damaged coil? What is its geometry? Does it look like a screw, or rather like a bolt? I'm really afraid to touch it now... 

Thanks! Any help is very much appreciated!

If this is a newer Etherwave and it uses the Coilcraft inductors then order directly from them when you order the tool (and buy more than one tool - they're cheap).

If the old core is extractable in any way (whole or in pieces) all you need to do is screw in a new core from the coil you buy without unsoldering and replacing the whole coil. But chances are that you will need to replace the whole coil.

If this is a newer Etherwave and it uses the Coilcraft inductors then order directly from them when you order the tool (and buy more than one tool - they're cheap).If the old core is extractable in any way (whole or in pieces) all you need to do is screw in a new core from the coil you buy without unsoldering and replacing the whole coil. But chances are that you will need to replace the whole coil.

Thanks pitts8rh, this is extremely helpful. 
I think I have found the item on Coilcraft:
https://www.coilcraft.com/en-us/products/rf/tunable-rf-inductors/vertical-mount/slot10/
One more question: do you think I can remove that piece just by pulling or is there a smart way?
Thanks.

"One more question: do you think I can remove that piece just by pulling or is there a smart way?" - bugo99

If you are talking about the ferrite core, you can't just pull it out.  The ferrite has external threads on it just like a fine-thread machine screw or bolt, and the sleeve that contains it is internally threaded, so the ferrite has to be turned out or alternatively broken into small pieces that can be shaken out.
 
I have (as an experiment that I don't recommend) used a vibrating engraving tool to pulverize a ferrite core into dust to save a non-replaceable coil.  This wasn't on a theremin but it was for a canned inductor like the Coilcraft part.  But the potential for damage to the rest of the board is so high that unsoldering and replacing the coil would be the preferred method.

The coil replacement is quite easy if you have a decent temperature-regulated soldering iron and can use solder wick or a solder sucker to clean excess solder out of the holes in the circuit board.  After doing that the part will usually still be stuck but you slowly work the coil off the board by heating each pin while gently pulling on the part, repeating as necessary around all the pins to slowly walk the part out.  If you don't finesse the removal however you can also tear the traces off the circuit board, so do this at your own risk or find someone with some experience with soldering and part removal.

If you just broke off the top half of the core, and the bottom half is intact, you can remove it by gluing a hex key to the top of it, and then unscrewing it.  Obviously this requires care not to get glue in the threads.