With locations in Punchh, deleting the store itself is not an option.
This is because there are many dependencies surrounding the store and data that would be lost.
For example:
Redemption Data
Account History
Purchase History
Transaction Data
If this data were to be removed, rewards, redemptions, transactions etc... would be removed as well. As such, deactivating a site is the ideal option. To learn how to do so, please see: How do I deactivate a location in the Platform that is now closed?