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Does anyone have the answer to this please?

I don't think you can disable that short of restricting the QuickTime app.

I was hoping to not hear that... has anyone experienced something similar in requirements of locking down screen recording on a mac? is it feasible in any way taking into consideration that quicktime is part of the OS?
Any suggestions are welcome.. any logic is welcome... any answer is welcome :)

I don't believe there's a way to do this, mostly because for it to be done with something like a defaults write command or a Config Profile, Apple has to add that in and support such a lock down feature. I know of nothing that disables that option within QuickTime. The fact that there is no GUI way of disabling it is also telling. Not that that means there isn't one, since there are many hidden preference options that don't show up in an app's preferences window, but, I don't see anything in relation to disabling that functionality. QuickTime Player doesn't even have a Preferences window. : /

If you can convince the powers that be that, if this is truly a requirement, you'll need to block the use of Quicktime altogether with Restricted Software, then that may be your best or only real option.

Just curious though, what exactly is the need here? Why do you need to stop this functionality? If you explain the situation further, it may help some of us think of some other approaches.