"Un-bounce" e-mail address in Campaigns

I have several clients where their e-mails bounced during a campaign. However, after discussions with them, they stated that these bounces were the result of system errors on their end.

I need to "un-bounce" the specific e-mail so they can receive our campaigns. I tried to fully delete the contacts in CRM and then re-sync to Campaign. Did not work. What should I do?