"Card offence" refers to actions or behaviors that violate the rules or regulations associated with using a card, such as a credit or debit card. Full definition
Essentially the player who commits the red card offence is considered to have been dismissed from that moment on, even though play continues and the red card has not yet been issued. (sbnation.com)
Previously this season he was in charge when we lost at home to Watford and when we won away at Palace, famously sending off Aaron Cresswell for two harsh / incorrect yellow card offences in one minute. (westhamway.net)
typical, not only was that a foul but it was a yellow card offence because he purposefully pulled on the other side. (justarsenal.com)