This was a requirement of Regs. E and DD until about 5 years ago. Just because the regs no longer require it, you're not finished yet.
At the time you & the affected customers switched to e-delivery, you probably used some type of formal agreement. If it was ESIGN-compliant, you told the customer what to do if s/he changed his/her email address. That same agreement may bind you to some course of action--such as switching from e-delivery to paper. Find & read the agreement before deciding whether bounce-back monitoring is necessary.
There's at least one other reason to act. If email is an element of your marketing activity, you don't want a database full of non-working addresses.
_________________________
...gone fishing.