NEW YORK — American Express Co. said Monday its profit fell 24 percent in the third quarter as cardholders restrained their spending and had more trouble paying down debt. The results were better than anticipated, and propelled Amex’s shares higher. Still, the company’s report echoed other recent results showing that the credit-card environment is worsening. The credit card issuer said net income was $815 million, or 70 cents a share, in the July to September period, down from $1.07 billion, or 90 cents a share, in the same time frame last year.