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1. Other user shares their screen.
2. You request control or other user gives you control of the shared screen.
3. When you click on the shared screen, the Teams taskbar (with the mute, hang up, etc. options) disappears and clicks and mouse movement are not registered in the other person's desktop.

The workaround that works consistently is to click "Activity" in the top-left, then to select the meeting again from the thumbnail.  At this point, the cursor with your icon will show up and you'll be able to control the other person's desktop.

Pinning or unpinning apps in the left-hand sidebar of the Web or Desktop Teams client gives users the following message before reverting the apps back to default: "Your admin has updated your settings. Some of your pinned apps may have moved".