No, you don’t need to keep the Kitconnect package in your store after the migration is complete.
Kitconnect is only used as a bridge to connect our migration tool to your store for reading and transferring data. Once the migration is finished, you can safely delete the Kitconnect folder from your website’s root directory. Removing it will not affect any of the data that has already been migrated to your new store.
If you need to run another migration in the future, you can simply upload the Kitconnect package again when needed.