Your gift card product cannot be deleted, but if you decide you don't want to sell gift cards any longer, you can disable their sale by going to STORE > Products > Gift Cards and clicking Disable.
When you disable gift cards, you can still view and manage any cards with existing balances, until all balances have been used. At that point, the gift card table becomes disabled. Also, the gift card option still displays at checkout so that customers with outstanding gift card balances can use them at checkout. Once all outstanding balances are redeemed, the gift card payment option no longer displays.