Presuming that you purchased the ticket in Israel and that the CC was issued by an Israeli bank (or Israeli issuer for a non-Israeli bank), Israeli law will most likely apply. Thus, you will need to check Israeli law for the actual process.
In the first instance, you note that while the debit was imposed by the carrier, you only spoke with eDreams. I am presuming that you have spoken directly with the carrier too. If you haven't, it's important to call the carrier first to determine what the carrier says went wrong.
While most CC issuers provide chargeback protections whether or not they are required to by local law, you are correct that there are potential concerns here if this situation spins out-of-control (which it would not in most countries).
1. Unfortunately, it is the carrier which you apparently authorized to debit your CC, not eDreams. Thus, your dispute is with the carrier. If the carrier can document the basis for its charges and the CC issuer denies the chargeback attempt, you will then owe the balance to the CC issuer.
2. If, on the other hand, the carrier really believes that you owe the undiscounted amount, but the bank sustains the chargeback attempt, the carrier could either cancel your itinerary or simply put it into an "add collect" status such that a BP won't be issued until you pay the difference.
I would hope that Israeli authorities would assist you in this matter because if it happened to you, it more than likely is not a one-off and has happened to others. If you (and others) don't report it, nobody will ever take action.
Not that you need a lecture here, but because FT is a public board, the real lesson here is that nothing is "free." Before you work through third-party vendors, make sure that you have fully researched them, that they have a good reputation, are known for good customer service and that the terms & conditions they impose are reasonable. It is also important to look carefully at the discount / savings they offer. To be frank, you are trading off money for protections and customer service. Is it really worth it once you add up all of the risks?