If the contract was entered into in the United States, by a U.S. resident, through a U.S. website, with a U.S. corporation (Marriott), using a U.S. credit card, and other similar factors, there are certainly choice of law principles and arguments in favor of the domestic (U.S.) forum.

Where in the contract is it stated that the exclusive place of dispute resolution is in Greece?

Even if this were so, there may be contrary forum selection or venue clauses in the credit card terms & conditions (disputes with bank), Marriott website (Utah?), and the consumer protection laws themselves, among other possibilities.

Choice of law issues are seldom simple.

"Those who sleep on their rights lose them" (laches) applies to filing a timely credit-card chargeback / dispute.

"You snooze, you lose!"