One possible workaround is adding a Declined recognition level for the constituent, which will remove the Recognition Program level from the Constituent Recognition Data List and over to the Constituent Recognition Declined Levels By Program Data List. This functionality is documented in the CRM User Guide's Declined Recognition Levels entry

Further, there is an Idea Portal suggestion to add this functionality in a future service pack, which can be found at the following URL: https://bbcrm.ideas.aha.io/ideas/CRM-I-2608