If you set the LOGO_URL MFE setting (which after Olive you should be able to do via dynamic configuration), that should get you a different logo. Have you tried that, yet?
Yes: this is an item in the soon-to-be-released Olive Release Notes. All you need to do is set FEATURES['ENABLE_AUTHN_MICROFRONTEND'] to False in the openedx-lms-production-settings template patch in a custom Tutor plugin (you can look at cookiecutter-tutor-plugin as an example).
Edit (again):
Actually, just running tutor config save --set MFE_AUTHN_MFE_APP=null would be the simplest possible way, as instructed in the tutor-mfe README.