I would first confirm that your colleague is running and joining the Zoom meeting with the downloaded and installed Zoom application versus a Web Browser. I just ran into this issue with a couple of folks I support, and simply changing to using the Zoom Application solved the gre
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Second: Go to the Share Screen Settings in the Zoom app and click on the Advanced Button on the bottom. I first confirm that under Use hardware Acceleration for section that Screen Sharing is checked.
If the grey boxes still appear then I would recommend to click on the | ••• | on the toolbar and select Hide Floating Meeting Controls. They will go away in 1 to 3 seconds, but it's possible that they show-up, again. Not sure what causes this.
If the grey boxes continue to pop-up on the attendee screens, I would highly recommend a dual monitor computer configuration. This will give you the ability to click-n-drag the toolbar and other windows to the other monitor.
Also, keep in mind that through these above steps the grey boxes may stop showing on the Attendees Screens, but the presenter may think it is still a problem. This is due to the presenter is still seeing the Toolbar and others windows, although the attendees are not.