Publication shows up in secondary server
When you've restored the database on the secondary you actually moved all its properties, including the fact it's a publisher. In this case you don't have a working replication, just the attributes for replication enabled. So this won't let you drop the db as you want.

The simplest way to remove replication metadata for this db is by using the system stored procs:

-- ON THE PUBLISHER
use YourDb
Go

exec sp_cleanupdbreplication
exec sp_removedbreplication
GO


Just make sure you're running this script on the secondary, the one you want to drop, not on the production db.