LemonTorque: The day after entering the details of a new credit card on GOG, my bank locked the account due to a suspicious purchase ([url moderated]) originating in Cyprus, where I understand GOG process their card payments. This seems like a very suspicious coincidence and I will no longer trust GOG with my card details.
I recommend using the safer payment options if you're concerned by this.
Whenever unusual activity occurs on a credit card bank security departments act with caution, this is normal. GOG's payment processor is in Cyprus, and unrelated to that there is a lot of fraudulent activity made by others in the world that pass through Cyprus also, and banks know this so when they see a new payment going through Cyprus for the first time they may err on the side of caution and disallow the transaction until the owner of the account confirms that it is a legitimate transaction being made and not fraud or card theft.
You need to communicate with your bank that the transactions to GOG are legitimate and not fraudulent, and they will put this on record and allow payments to GOG in the future without triggering security alerts over the transaction.
This isn't unique to Cyprus, but this can happen whenever any bank detects a transaction that is statistically unusual for the card holder to make compared to past habits, or if any other statistically relevant risk factors exist where they are unable to determine the legitimacy of the transaction on their own. They are likely to err on the side of caution until the card holder informs them that they did in fact make the transaction and it is legitimate.
There is nothing unsafe about GOG processing payments in Cyprus.