Grease can only be applied before you connect the socket.
You either have a melted plug, or it is just incredibly seized... which I’ve never seen one that stuck.
If it has shorted and melted on, you’re probably going to have to replace the plug/socket completely. If it has melted, you may be able to see some melting damage on the outside.
If you think it’s just stuck, you can try GENTLY knocking the plug with the end of a screwdriver (or similar small lightweight tool). But you have to be VERY careful not to hit it hard because you could easily break something. You can also pick up a can of electric motor cleaner/lubricant. They are lubricants that are formulated to be non-conductive. Final solution if it’s stuck, you can try gently heating the plug with a heat gun. Again, you have to be very careful that you don’t overheat it and heat it. If you do, then you’ll have to replace it.