Received a legal citation from a credit card company. Said to respond in writing by next Monday. If I do not respond, what will happen?

What can the credit card company do to me if I do not respond to their legal citation?

A citation usually means some sort of minor quasi-criminal charge. That would not be from a credit card company.

But perhaps that's what they call a summons in your area. If so, anyway, they would be able to get a default judgment against you. Then, with a judgment, they would be able to seize your non-exempt property and garnish a portion of your wages to satisfy the debt.