Why do they even pretend to give a reason anymore. Just close it. Nobody is buying the "hate speech" "adult sexual exploitation" whatever arguments, and honestly it just makes facebook look like liars. Just delete the group and say: "It violated our terms of service". That's probably also a lie, but at least it's a little less obnoxious.
If you manage a community that is even remotely controversial, you’d better start asking your community for their email address, as an emergency backup. Possibly even ask for their phone number. Though it's tempting, don't message them at all. Just hang onto it. Only use it to if your community is banned and you need to start over somewhere else. Then email/text them the location of the new community.
Keeping a record of phone numbers or email is asking for trouble when you get audited. Keep it more random than that and encrypted.