Yes, this can be done -but- it will really depend on the gateway & merchant account reporting tools provided by your merchant processor. This is an area that varies widely from one processor to another.
For instance, we can view the Interchange category that applies to any settled transaction run by any of our merchants and this same level of detail is made available to them on the real-time merchant reporting system that we setup for each of them.
Some Payment Gateway systems like Authorize.Net also provide a fairly descriptive summary of each transaction processed.
Lastly, some front-end processing networks offer a Merchant Viewing tool that will give you the same kind of information, albeit usually at a small additional cost.
My suggestion is to ask your merchant processor whether they can supply you with reporting options similiar to the above in an online viewing system of some kind so that you can check any time you want.
Failing that, you might be able to call up their merchant support department and ask them about a particular transaction and most of the time - their customer support reps should be able to look up the transaction and let you know whether it was a credit or debit transaction.
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