Hi Jake Bigelow,
Thanks for posting here, I’m very willing to help you😊
I recommend you login Teams web client as a workaround firstly, on Teams web client, if you maximize the window, it will appear at Application Window tab, if you minimize, it will disappear.
There are no settings to control this, please try to open these windows before you share the screen to see if it will appear. Then check the update of your Teams (click your profile->Check for update).
Meanwhile, please try to do the following steps to clean Teams cache, and check the result
· Quit Microsoft Teams if it show on the status bar.
· Copy and paste the following location (%appdata%\Microsoft\Teams) into File Explorer.
· Delete contents of the entire folder.
· Restart Microsoft Teams.
Also you can try to check with a different device or you can create a new windows user account to see if the issue persist.
Any update will be appreciated.
Best regards,
Regina