I got a problem when a non-Administrator user tries to remove an Opportunity team member.
I checked the Salesforce documentation, 3 condictions are necessary in order to do that: 1. ”Read” on users 2. "Edit” on opportunities 3. Owner of the opportunity, or above the owner in your organization’s role hierarchy
My use case is a standard user (not Administrator) who owns the Opportunity (condition 3 verified). His profile allows the update of Opportunities (Opportunity EDIT permission is checked: condition 2 checked).
Regarding condition 1, I didn't find any EDIT Permission on the object User, but my Organization Wide defaults settings for Users are 'Puclic Read Only'.