You can verify a BIC or look up a BIC for a particular bank using this Transferwise tool
I would have thought IBAN was more important than BIC. That identifies your specific account and includes within it the country code, the bank identifier and the branch identifier as well as the account number. You can use this XE IBAN decoder
to decipher an IBAN into its constituent parts.
From experience of a friend who experienced problems transferring funds to the Cooperative Bank of Chania, which is part of the same cooperative group as Pancretan, the problem is often with the corresponding bank, usually either The Bank of Greece or The National Bank of Greece. I don't think that the cooperative banks act as corresponding banks in the Swift system so the funds route through an intermediary. The problem is often with the intermediary bank. The major banks, i.e. Alpha, Eurobank, NBG and Piraeus act directly as corresponding banks so do not use an intermediary. If the problem is there the funds should be returned so you should check back with the exchange company.Transferwise
claim not to use the Swift system to transfer funds so it might be worth trying them instead of your current exchange company. I would be amazed if the rates were worse.