Not a service I've seen offered. I recently fitted a new starter from Electrex to my 907ie for £99 delivered. At that price I doubt if refurbishing the old one is cost effective.
https://www.electrexworld.co.uk/acatalog/Online_Catalogue_Starter_Motors_705-p2.html Fits most Ducatis (not Pantahs or bevels).
This one should fit but you may have to swap over the drive pinion as the ratio changed around 2010. https://www.mymotoparts.co.uk/p/sta...isXDrMwt9U396YJ0tLpD9aLYKV8bjMR8aAjM5EALw_wcB
Sorry, I don't understand what you mean by "no gear". If there are no gear teeth, how can the starter operate?