It is considered a best practice to make sure you delete recpients from your mailing list who generate nothing for you but bounced emails.
Continuation to email bounced contacts can lead the ISP of that email address to believe you may be a spammer who has poor contact management habits and is not interested in removing potentially non-existant email addresses.
Likewise, if an email is sent in bulk to many people and the majority of them from one ISP simply bounce in quick succession, the ISP may believe you are trying to gauge if certain addresses exist or not and subsequently block any further emails from you.
The below video will show you how to remove email addresses from your mailing list that generate bounces, while the text guide below it will walk you through in a step-by-step manner:
The ekmResponse system will automatically remove users who have bounced 3 times, but it is generally regarded that contacts should be removed if they bounce twice.
The first occasion may be isolated to a temporary full mailbox, but any further bounces mean the mailbox either doesn't exist, has specific spam fitlering rules or is still full. Afterall, what is the point in emailing a 50mb mailbox that is always full? Your emails would be better sent to a new user who has opted in to receive your emails than to someone who doesn't check their mailbox.
To delete bounced contacts, you need to view the statistics page of the email campaign.
In the "bounced contacts" section, you will see a link that reads "Delete All":
...which when clicked on, a pop-up will appear asking how many times the recipients to be deleted should have bounced the email:
Please note that ALL contacts across ALL your contact groups will be deleted if they have bounced the amount of times, or more, that you enter into the input field. The prompt is not purely just for the campaign you are viewing.
If you do not wish to delete all bounced contacts, then you can just delete users individually. This is done by clicking the red corsses underneath the "Delete All" option, against the respective user.