Hmmm, something very wrong there. It appears the starter has not been throwing correctly into mesh, I assume the starter was bolted in tight/straight? Now, this issue of starter contacts although being a common problem and easy to repair I have seen the WRONG contact kit fitted. The contacts are connected when the solenoid pulls a plunger which acts as a 'bridge to short the contacts, now, as this is happening the plunger also has a rod attached, this rod pushes the starter gear into mesh, if the 'throw' is correct the starter gear will be in full contact with the flywheel (big wheel with teeth inside housing) at the same time as the plunger shorts the contacts and spins the starter motor. There are a variety of kits with different style/type of contacts and perhaps more importantly different length rods that move the starter gear. It is possible you have the wrong plunger/kit which could result in the starter gear just starting to turn as the contacts connected, this would result in more wear ect and could cause a problem such as yours. Of course the bearings ect shold be checked for play but whatever you choose, if you decide to rebuild that particular started first check that the starter is the right one for your car unlikely not to be but worth checking and then buy any parts based on the starter number and NOT on your chassis number. The reason for that is there are many 12 and 24 volt variations of these starters which will bolt right in but will not be operating at their optimum, BTW, how many teeth on that starter gear I ask only because I cannot see all of them? If you are talking about inside the bellhousing on the engine then clean and grease free is fine, the bearings on the starter are sealed units and if leaking/noisey then replace them.
regards
Dave