Generally speaking, the insurance companies for travel insurance only reimburse a) non-refundable portions and b) do not allow you to double-dip. In the case of airline tickets they will almost assuredly contact Delta (or you have to submit proof of the cancellation/refund) in which case Delta will clearly indicate a credit. Unless you purchased fully refundable tickets, that is. You will end up getting the Delta eCredit, and the insurance carrier will NOT reimburse you cash. HOWEVER, *most* insurance carriers allow a certain timeframe. So if you do NOT use the eCredit from Delta, and it expires after the 1 year, THEN you can (typically, not guaranteed) go to the insurance carrier and THEN they will refund you the amount in cash.

To be fair, this question isn't Delta specific, but rather travel insurance related and should be moved to the travel insurance area (IMO).