They may not do this unless you had previously agreed to let them use this credit card or account whenever there was a balance due and owing to them. You might check or review any agreements or contracts, to see if you did authorize them to do this.If you have not been injured--that is, they only took  the amount that you did owe--there is effectively no legal recourse for that they did (the U.S. legal system generally only provides recourse for loss or harm, not simply for a violation of rights), though you should consider not renting from or doing business again with a place that saves card numbers and feels free to use them later.