For anyone who finds themself in this situation and is confused about how to remove the group identifier from the old account, the trick is to switch to App Groups from the filter on the right on the "Identifiers" page of "Certificates, Identifiers & Profiles". By default, it only shows App IDs.
This link should go their directly:
https://developer.apple.com/account/resources/identifiers/list/applicationGroup
Topic:
Code Signing
SubTopic:
Certificates, Identifiers & Profiles
Tags: