Sorry to hear, is it the first video noise that is back?
If it is, then its the starter.
My s2000 suffers from the starter motor grind, its a common issue where when you go to start the engine, the bendix gear pops out and attaches itself to the teeth of the flywheel and rotates the engine to start. However there is a known issue where the bendix gear is lazy to retract and stays on the flywheel for abit longer and causes the grind noise.
My s2000 suffered from it. I changed the starter motor and it disappeared. Apparently Honda has not superseded the starter motor and therefore it is a common issue.
Usually more apparent when the weather is cold.
If you google "s2000 starter grind" many threads on s2ki about this
The k20 engines, use the same starter motor as the s2000
See very last post on this thread
UK & Ireland S2000 Community - Starter Motor Grind On Cold Mornings - Hi Guys, After searching various threads, I have come to the conclusion that this issue is a common quirk with the s2000. Apologies again for raising another thread on the issue. I have just started to notice it now after the...
www.s2ki.com
I think its a lubrication issue of the bendix gear, where it slides on the shaft to pop out gets dry.
If you can remove your starter you can try servicing it an lubricating it. Although easier to buy a new starter.
OEM honda is like £400+ so third party makes are usually ok. Try Blueprint.
You could live with it and I guess it will do no harm, but it does look awkward every time you start the car.
It would seem like your an amateur, lol.
It may be a damaged flywheel also perhaps?