Do you reach out to customers after they file a chargeback?

I'm wondering, once someone has initiated a chargeback, should you keep trying to resolve the issue directly or turn over everything to the dispute process and just forget about it? There have been cases where customers did not understand what chargebacks were all about while in some other cases customers were willing to cooperate.

Does anyone have a standard workflow for post chargeback communication and what happens after the customer starts the dispute process?