No your organization cannot see information that you send on your personal Teams account(s).
What information can my organization see when I enroll my device?
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If this is helpful please accept answer.
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I have my organization Intune installed and Microsoft teams is installed with my organization and my personal teams too in iOs. In my personal account I communicate with my family and friends and discuss many things. Does my organization teams able to collect the data of my personal teams account or school organization teams account too?
No your organization cannot see information that you send on your personal Teams account(s).
What information can my organization see when I enroll my device?
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If this is helpful please accept answer.