Hello @Christopher Travis
The error message indicates that the source server doesn't have write permission to the target DC, which usually indicates that the target forest isn't an account partition of the source forest, and the user has insufficient access rights.
Based on the error message, it seems like the MI you are using doesn't have the necessary permissions to perform the remove-distributiongroupmember
cmdlet.
You mentioned that you have Exchange Administrator access added to this MI, but it's possible that the MI doesn't have the necessary permissions to perform this specific cmdlet.
I would recommend checking the permissions of the MI and ensuring that it has the necessary permissions to perform the remove-distributiongroupmember
cmdlet.
You may also want to check the Exchange Online module documentation to see if there are any specific permissions required for this cmdlet.