Offline transactions are where the merchant doesn't process the payment at the time, and instead the transaction is processed around 24 hours later (it can even sometimes take up to a week). The merchant is the one to decide if the transaction will be online or offline (wherever possible, we push the transaction online). It means that the merchant doesn't send a message to your bank via Curve, and instead takes the risk that you are good for the money, and only charges you a day or two later.
It also means that the first Curve hears about this transaction is several days later, at which point we send a notification and charge the card that you have selected on Curve. When the offline transaction comes in, there's nothing marking it as having taken place several days before, so we can't match it with the underlying card that you had selected at the time of making the transaction.
You can also get an offline transaction for a previous online transaction. For example, a retailer may approve a transaction on your card so we charge your underlying card. If the retailer then doesn't collect the funds after 7 days, we'll refund the money. Occasionally the retailer will then decide to claim the money several days later, so they'd need to create an offline transaction. It will be charged to whatever card you have selected at the time that they send the transaction to us.
Some restaurants in the US use offline transactions to handle charging for tips. What happens is that the initial payment (minus tip) is processed as an authorisation at the time you present your card to pay, and then the restaurant charges for the meal + tip the following day (or even later) in a separate offline transaction, which means that for a short time you are charged twice. The funds for first charge (without the tip) is never collected by the restaurant so it is refunded by us after 7 days - we're always happy to speed up the process for you and reverse it manually on our end if you just let us know.
Another example is if you buy something abroad, you may be charged in GBP or USD, refunded and then later re-charged in the local currency. We've noticed this issue to be fairly common with merchants in Japan. What happens is they firstly preauthorise the transaction amount on your card (often in USD), which then reverses automatically after 7 days. The merchant will then capture the full amount in JPY offline, often up to a couple of weeks from the original transaction. For a short time, you may see both transactions on your account while one is being refunded by the merchant.