Mikhail your issue should not be related to OAUTH or Exchange but to mail flow.
When you create a meeting in Microsoft Teams and your mailbox resides on-premises, MS Teams backend service will send an appointment e-mail to your on-premises mailbox. If that e-mail can't be delivered, because of not properly configured mail flow between Exchange Online and Exchange on-premises, the meeting will not be scheduled. The effect that you see in that case is that in MS Teams client the user creates the meeting and sees the meeting to be grayed out for a certain time. After around 30 seconds, the meeting disappears as the MS Teams backend service didn't receive any response from your on-premises mailbox..
Please have a look and let me know if that could help you solve your issue
Kind regards
Spikar