When removing a user/team member from one of your applications, you just need to double check that the API keys that are being used in your search implementation or the extension configuration settings are not the ones that belong to that user.
This is because all API keys associated with that user will be deleted when the user is removed, and if the application is depending on their keys, it will break.
It's possible for you to see which keys are associated with those users on the API keys page ("All API keys" tab) in the dashboard.
You just need to cross-reference the keys being used for your search implementation with those belonging to the users your are going to remove. There's no problem to remove them if they are not in use. If they are, then you'll will need to rotate / change the keys being used in production (i.e. use a different user's key) before removing those team members.
You can read more about the best practices for your API keys here.