If she doesn't have responsibility for this, she just shouldn't respond. The transition team should have responded. Or, she could have responded with "I'm contacting the transition team leader to escalate your issues as soon as possible" or similar. There is absolutely no excuse for responding to someone who has announced that they are quitting over very explicit grievances with "let's hop on a call to get some details". If ever there is a time to escalate, it is this.
To escalate, you need to have a better idea of the issues to know who to escalate to. Plus this is turning into a personal issue (quitting) so a forum isn't appropriate for that part. Asking to talk on the phone is a perfectly reasonable, appropriate, and sensitive way to find out more and figure out how to most helpfully address things. A phone call is the first step in escalation. I honestly don't understand your negative read here. Things don't get 100% addressed immediately in a single exchange. Communication is a back and forth process and this is an entirely appropriate initial response from a customer service manager.
